test/yuki/yuki_1720.test.cpp

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• Last update: 2025-03-24 22:41:21+09:00
• Problem: https://yukicoder.me/problems/no/1720

Depends on

• Convolution (convolution/convolution.hpp)
• NTT (convolution/ntt.hpp)
• Simple CSR (data_structure/simple_csr.hpp)
• Sparse Table (data_structure/sparse_table.hpp)
• Graph (CSR format) (graph/base.hpp)
• Binomial Coefficient (math/binomial.hpp)
• math/internal_math.hpp
• modint/base.hpp
• modint/modint.hpp
• template/debug_template.hpp
• template/int_alias.hpp
• template/io.hpp
• template/template.hpp
• template/utility.hpp
• Common Interval Decomposition Tree (tree/common_interval_decomposition_tree.hpp)

Code

#define PROBLEM "https://yukicoder.me/problems/no/1720"

#include "../../convolution/convolution.hpp"
#include "../../math/binomial.hpp"
#include "../../modint/modint.hpp"
#include "../../template/template.hpp"
#include "../../tree/common_interval_decomposition_tree.hpp"

namespace ebi {

using mint = modint998244353;

void main_() {
    int n, k;
    std::cin >> n >> k;
    std::vector<int> p(n);
    std::cin >> p;
    rep(i, 0, n) p[i]--;
    Binomial<mint> binom(n);
    common_interval_decomposition_tree permutation_tree(p);
    auto dfs = [&](auto &&self, int v) -> std::vector<mint> {
        auto node = permutation_tree.get_node(v);
        if (node.is_leaf()) {
            std::vector<mint> ret(k + 1, 0);
            ret[1] = 1;
            return ret;
        }
        std::vector<mint> ret(k + 1, 0), prev(k + 1, 0), sum(k + 1, 0);
        ret[0] = 1;
        prev[0] = 1;
        for (auto ch : node.child) {
            ret = convolution_naive(ret, self(self, ch));
            ret.resize(k + 1);
            if (node.is_linear()) {
                rep(i, 0, k) {
                    ret[i + 1] += sum[i];
                }
            }
            rep(i,0,k) {
                sum[i] += prev[i];
            }
            prev = ret;
        }
        ret.resize(k + 1);
        if (node.is_prime()) ret[1]++;
        return ret;
    };
    auto ans = dfs(dfs, permutation_tree.root_id());
    ans.resize(k + 1);
    rep(i, 1, k + 1) {
        std::cout << ans[i] << '\n';
    }
}

}  // namespace ebi

int main() {
    ebi::fast_io();
    int t = 1;
    // std::cin >> t;
    while (t--) {
        ebi::main_();
    }
    return 0;
}

#line 1 "test/yuki/yuki_1720.test.cpp"
#define PROBLEM "https://yukicoder.me/problems/no/1720"

#line 2 "convolution/convolution.hpp"

#include <algorithm>
#include <bit>
#include <vector>

#line 2 "convolution/ntt.hpp"

#line 4 "convolution/ntt.hpp"
#include <array>
#line 6 "convolution/ntt.hpp"
#include <cassert>
#line 8 "convolution/ntt.hpp"

#line 2 "math/internal_math.hpp"

#line 4 "math/internal_math.hpp"

namespace ebi {

namespace internal {

constexpr int primitive_root_constexpr(int m) {
    if (m == 2) return 1;
    if (m == 167772161) return 3;
    if (m == 469762049) return 3;
    if (m == 754974721) return 11;
    if (m == 998244353) return 3;
    if (m == 880803841) return 26;
    if (m == 924844033) return 5;
    return -1;
}
template <int m> constexpr int primitive_root = primitive_root_constexpr(m);

}  // namespace internal

}  // namespace ebi
#line 2 "modint/base.hpp"

#include <concepts>
#include <iostream>
#include <utility>

namespace ebi {

template <class T>
concept Modint = requires(T a, T b) {
    a + b;
    a - b;
    a * b;
    a / b;
    a.inv();
    a.val();
    a.pow(std::declval<long long>());
    T::mod();
};

template <Modint mint> std::istream &operator>>(std::istream &os, mint &a) {
    long long x;
    os >> x;
    a = x;
    return os;
}

template <Modint mint>
std::ostream &operator<<(std::ostream &os, const mint &a) {
    return os << a.val();
}

}  // namespace ebi
#line 2 "template/int_alias.hpp"

#include <cstdint>

namespace ebi {

using ld = long double;
using std::size_t;
using i8 = std::int8_t;
using u8 = std::uint8_t;
using i16 = std::int16_t;
using u16 = std::uint16_t;
using i32 = std::int32_t;
using u32 = std::uint32_t;
using i64 = std::int64_t;
using u64 = std::uint64_t;
using i128 = __int128_t;
using u128 = __uint128_t;

}  // namespace ebi
#line 12 "convolution/ntt.hpp"

namespace ebi {

namespace internal {

template <Modint mint, int g = internal::primitive_root<mint::mod()>>
struct ntt_info {
    static constexpr int rank2 =
        std::countr_zero((unsigned int)(mint::mod() - 1));

    std::array<mint, rank2 + 1> root, inv_root;

    ntt_info() {
        root[rank2] = mint(g).pow((mint::mod() - 1) >> rank2);
        inv_root[rank2] = root[rank2].inv();
        for (int i = rank2 - 1; i >= 0; i--) {
            root[i] = root[i + 1] * root[i + 1];
            inv_root[i] = inv_root[i + 1] * inv_root[i + 1];
        }
    }
};

template <Modint mint> void fft2(std::vector<mint>& a) {
    static const ntt_info<mint> info;
    int n = int(a.size());
    int bit_size = std::countr_zero(a.size());
    assert(n == 1 << bit_size);
    for (int bit = bit_size - 1; bit >= 0; bit--) {
        int m = 1 << bit;
        for (int i = 0; i < n; i += 2 * m) {
            mint w = 1;
            for (int j = 0; j < m; j++) {
                mint p1 = a[i + j];
                mint p2 = a[i + j + m];
                a[i + j] = p1 + p2;
                a[i + j + m] = (p1 - p2) * w;
                w *= info.root[bit + 1];
            }
        }
    }
}

template <Modint mint> void ifft2(std::vector<mint>& a) {
    static const ntt_info<mint> info;
    int n = int(a.size());
    int bit_size = std::countr_zero(a.size());
    assert(n == 1 << bit_size);

    for (int bit = 0; bit < bit_size; bit++) {
        for (int i = 0; i < n / (1 << (bit + 1)); i++) {
            mint w = 1;
            for (int j = 0; j < (1 << bit); j++) {
                int idx = i * (1 << (bit + 1)) + j;
                int jdx = idx + (1 << bit);
                mint p1 = a[idx];
                mint p2 = w * a[jdx];
                a[idx] = p1 + p2;
                a[jdx] = p1 - p2;
                w *= info.inv_root[bit + 1];
            }
        }
    }
}

template <Modint mint> void fft4(std::vector<mint>& a) {
    static const ntt_info<mint> info;
    const u32 mod = mint::mod();
    const u64 iw = info.root[2].val();
    int n = int(a.size());
    int bit_size = std::countr_zero(a.size());
    assert(n == 1 << bit_size);
    int len = bit_size;
    while (len > 0) {
        if (len == 1) {
            for (int i = 0; i < n; i += 2) {
                mint p0 = a[i];
                mint p1 = a[i + 1];
                a[i] = p0 + p1;
                a[i + 1] = p0 - p1;
            }
            len--;
        } else {
            int m = 1 << (len - 2);
            u64 w1 = 1, w2 = 1, w3 = 1, iw1 = iw, iw3 = iw;
            for (int i = 0; i < m; i++) {
                for (int j = 0; j < n; j += 4 * m) {
                    int i0 = i + j, i1 = i0 + m, i2 = i1 + m, i3 = i2 + m;
                    u32 a0 = a[i0].val();
                    u32 a1 = a[i1].val();
                    u32 a2 = a[i2].val();
                    u32 a3 = a[i3].val();
                    u32 a0_plus_a2 = a0 + a2;
                    u32 a1_plus_a3 = a1 + a3;
                    u32 a0_minus_a2 = a0 + mod - a2;
                    u32 a1_minus_a3 = a1 + mod - a3;
                    a[i0] = a0_plus_a2 + a1_plus_a3;
                    a[i1] = a0_minus_a2 * w1 + a1_minus_a3 * iw1;
                    a[i2] = (a0_plus_a2 + 2 * mod - a1_plus_a3) * w2;
                    a[i3] = a0_minus_a2 * w3 + (2 * mod - a1_minus_a3) * iw3;
                }
                w1 = w1 * info.root[len].val() % mod;
                w2 = w1 * w1 % mod;
                w3 = w2 * w1 % mod;
                iw1 = iw * w1 % mod;
                iw3 = iw * w3 % mod;
            }
            len -= 2;
        }
    }
}

template <Modint mint> void ifft4(std::vector<mint>& a) {
    static const ntt_info<mint> info;
    const u32 mod = mint::mod();
    const u64 mod2 = u64(mod) * mod;
    const u64 iw = info.inv_root[2].val();
    int n = int(a.size());
    int bit_size = std::countr_zero(a.size());
    assert(n == 1 << bit_size);
    int len = (bit_size & 1 ? 1 : 2);
    while (len <= bit_size) {
        if (len == 1) {
            for (int i = 0; i < n; i += 2) {
                mint a0 = a[i];
                mint a1 = a[i + 1];
                a[i] = a0 + a1;
                a[i + 1] = a0 - a1;
            }
        } else {
            int m = 1 << (len - 2);
            u64 w1 = 1, w2 = 1, w3 = 1, iw1 = iw, iw3 = iw;
            for (int i = 0; i < m; i++) {
                for (int j = 0; j < n; j += 4 * m) {
                    int i0 = i + j, i1 = i0 + m, i2 = i1 + m, i3 = i2 + m;
                    u64 a0 = a[i0].val();
                    u64 a1 = w1 * a[i1].val();
                    u64 a2 = w2 * a[i2].val();
                    u64 a3 = w3 * a[i3].val();
                    u64 b1 = iw1 * a[i1].val();
                    u64 b3 = iw3 * a[i3].val();
                    u64 a0_plus_a2 = a0 + a2;
                    u64 a1_plus_a3 = a1 + a3;
                    u64 a0_minus_a2 = a0 + mod2 - a2;
                    u64 b1_minus_b3 = b1 + mod2 - b3;
                    a[i0] = a0_plus_a2 + a1_plus_a3;
                    a[i1] = a0_minus_a2 + b1_minus_b3;
                    a[i2] = a0_plus_a2 + mod2 * 2 - a1_plus_a3;
                    a[i3] = a0_minus_a2 + mod2 * 2 - b1_minus_b3;
                }
                w1 = w1 * info.inv_root[len].val() % mod;
                w2 = w1 * w1 % mod;
                w3 = w2 * w1 % mod;
                iw1 = iw * w1 % mod;
                iw3 = iw * w3 % mod;
            }
        }
        len += 2;
    }
}

}  // namespace internal

}  // namespace ebi
#line 9 "convolution/convolution.hpp"

namespace ebi {

template <Modint mint>
std::vector<mint> convolution_naive(const std::vector<mint>& f,
                                    const std::vector<mint>& g) {
    if (f.empty() || g.empty()) return {};
    int n = int(f.size()), m = int(g.size());
    std::vector<mint> c(n + m - 1);
    if (n < m) {
        for (int j = 0; j < m; j++) {
            for (int i = 0; i < n; i++) {
                c[i + j] += f[i] * g[j];
            }
        }
    } else {
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
                c[i + j] += f[i] * g[j];
            }
        }
    }
    return c;
}

template <Modint mint>
std::vector<mint> convolution(const std::vector<mint>& f,
                              const std::vector<mint>& g) {
    if (f.empty() || g.empty()) return {};
    if (std::min(f.size(), g.size()) < 60) return convolution_naive(f, g);
    int n = (int)std::bit_ceil(f.size() + g.size() - 1);
    std::vector<mint> a(n), b(n);
    std::copy(f.begin(), f.end(), a.begin());
    std::copy(g.begin(), g.end(), b.begin());
    internal::fft4(a);
    internal::fft4(b);
    for (int i = 0; i < n; i++) {
        a[i] *= b[i];
    }
    internal::ifft4(a);
    a.resize(f.size() + g.size() - 1);
    mint inv_n = mint(n).inv();
    for (auto& x : a) x *= inv_n;
    return a;
}

}  // namespace ebi
#line 2 "math/binomial.hpp"

#line 7 "math/binomial.hpp"
#include <ranges>
#line 9 "math/binomial.hpp"

#line 11 "math/binomial.hpp"

namespace ebi {

template <Modint mint> struct Binomial {
  private:
    static void extend(int len = -1) {
        int sz = (int)fact.size();
        if (len < 0)
            len = 2 * sz;
        else if (len <= sz)
            return;
        else
            len = std::max(2 * sz, (int)std::bit_ceil(std::uint32_t(len)));
        len = std::min(len, mint::mod());
        assert(sz <= len);
        fact.resize(len);
        inv_fact.resize(len);
        for (int i : std::views::iota(sz, len)) {
            fact[i] = fact[i - 1] * i;
        }
        inv_fact[len - 1] = fact[len - 1].inv();
        for (int i : std::views::iota(sz, len) | std::views::reverse) {
            inv_fact[i - 1] = inv_fact[i] * i;
        }
    }

  public:
    Binomial() = default;

    Binomial(int n) {
        extend(n + 1);
    }

    static mint f(int n) {
        if (n >= (int)fact.size()) [[unlikely]] {
            extend(n + 1);
        }
        return fact[n];
    }

    static mint inv_f(int n) {
        if (n >= (int)fact.size()) [[unlikely]] {
            extend(n + 1);
        }
        return inv_fact[n];
    }

    static mint c(int n, int r) {
        if (r < 0 || n < r) return 0;
        return f(n) * inv_f(r) * inv_f(n - r);
    }

    static mint neg_c(int k, int d) {
        assert(d > 0);
        return c(k + d - 1, d - 1);
    }

    static mint p(int n, int r) {
        if (r < 0 || n < r) return 0;
        return f(n) * inv_f(n - r);
    }

    static mint catalan_number(int n) {
        return c(2 * n, n) * inv(n + 1);
    }

    static mint inv(int n) {
        return inv_f(n) * f(n - 1);
    }

    static void reserve(int n) {
        extend(n + 1);
    }

  private:
    static std::vector<mint> fact, inv_fact;
};

template <Modint mint>
std::vector<mint> Binomial<mint>::fact = std::vector<mint>(2, 1);

template <Modint mint>
std::vector<mint> Binomial<mint>::inv_fact = std::vector<mint>(2, 1);

}  // namespace ebi
#line 2 "modint/modint.hpp"

#line 5 "modint/modint.hpp"

#line 7 "modint/modint.hpp"

namespace ebi {

template <int m> struct static_modint {
  private:
    using modint = static_modint;

  public:
    static constexpr int mod() {
        return m;
    }

    static constexpr modint raw(int v) {
        modint x;
        x._v = v;
        return x;
    }

    constexpr static_modint() : _v(0) {}

    template <std::signed_integral T> constexpr static_modint(T v) {
        long long x = (long long)(v % (long long)(umod()));
        if (x < 0) x += umod();
        _v = (unsigned int)(x);
    }

    template <std::unsigned_integral T> constexpr static_modint(T v) {
        _v = (unsigned int)(v % umod());
    }

    constexpr unsigned int val() const {
        return _v;
    }

    constexpr unsigned int value() const {
        return val();
    }

    constexpr modint &operator++() {
        _v++;
        if (_v == umod()) _v = 0;
        return *this;
    }
    constexpr modint &operator--() {
        if (_v == 0) _v = umod();
        _v--;
        return *this;
    }

    constexpr modint operator++(int) {
        modint res = *this;
        ++*this;
        return res;
    }
    constexpr modint operator--(int) {
        modint res = *this;
        --*this;
        return res;
    }

    constexpr modint &operator+=(const modint &rhs) {
        _v += rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    constexpr modint &operator-=(const modint &rhs) {
        _v -= rhs._v;
        if (_v >= umod()) _v += umod();
        return *this;
    }
    constexpr modint &operator*=(const modint &rhs) {
        unsigned long long x = _v;
        x *= rhs._v;
        _v = (unsigned int)(x % (unsigned long long)umod());
        return *this;
    }
    constexpr modint &operator/=(const modint &rhs) {
        return *this = *this * rhs.inv();
    }

    constexpr modint operator+() const {
        return *this;
    }
    constexpr modint operator-() const {
        return modint() - *this;
    }

    constexpr modint pow(long long n) const {
        assert(0 <= n);
        modint x = *this, res = 1;
        while (n) {
            if (n & 1) res *= x;
            x *= x;
            n >>= 1;
        }
        return res;
    }
    constexpr modint inv() const {
        assert(_v);
        return pow(umod() - 2);
    }

    friend modint operator+(const modint &lhs, const modint &rhs) {
        return modint(lhs) += rhs;
    }
    friend modint operator-(const modint &lhs, const modint &rhs) {
        return modint(lhs) -= rhs;
    }
    friend modint operator*(const modint &lhs, const modint &rhs) {
        return modint(lhs) *= rhs;
    }

    friend modint operator/(const modint &lhs, const modint &rhs) {
        return modint(lhs) /= rhs;
    }
    friend bool operator==(const modint &lhs, const modint &rhs) {
        return lhs.val() == rhs.val();
    }
    friend bool operator!=(const modint &lhs, const modint &rhs) {
        return !(lhs == rhs);
    }

  private:
    unsigned int _v = 0;

    static constexpr unsigned int umod() {
        return m;
    }
};

using modint998244353 = static_modint<998244353>;
using modint1000000007 = static_modint<1000000007>;

}  // namespace ebi
#line 1 "template/template.hpp"
#include <bits/stdc++.h>

#define rep(i, a, n) for (int i = (int)(a); i < (int)(n); i++)
#define rrep(i, a, n) for (int i = ((int)(n)-1); i >= (int)(a); i--)
#define Rep(i, a, n) for (i64 i = (i64)(a); i < (i64)(n); i++)
#define RRep(i, a, n) for (i64 i = ((i64)(n)-i64(1)); i >= (i64)(a); i--)
#define all(v) (v).begin(), (v).end()
#define rall(v) (v).rbegin(), (v).rend()

#line 2 "template/debug_template.hpp"

#line 4 "template/debug_template.hpp"

namespace ebi {

#ifdef LOCAL
#define debug(...)                                                      \
    std::cerr << "LINE: " << __LINE__ << "  [" << #__VA_ARGS__ << "]:", \
        debug_out(__VA_ARGS__)
#else
#define debug(...)
#endif

void debug_out() {
    std::cerr << std::endl;
}

template <typename Head, typename... Tail> void debug_out(Head h, Tail... t) {
    std::cerr << " " << h;
    if (sizeof...(t) > 0) std::cerr << " :";
    debug_out(t...);
}

}  // namespace ebi
#line 2 "template/io.hpp"

#line 5 "template/io.hpp"
#include <optional>
#line 7 "template/io.hpp"

namespace ebi {

template <typename T1, typename T2>
std::ostream &operator<<(std::ostream &os, const std::pair<T1, T2> &pa) {
    return os << pa.first << " " << pa.second;
}

template <typename T1, typename T2>
std::istream &operator>>(std::istream &os, std::pair<T1, T2> &pa) {
    return os >> pa.first >> pa.second;
}

template <typename T>
std::ostream &operator<<(std::ostream &os, const std::vector<T> &vec) {
    for (std::size_t i = 0; i < vec.size(); i++)
        os << vec[i] << (i + 1 == vec.size() ? "" : " ");
    return os;
}

template <typename T>
std::istream &operator>>(std::istream &os, std::vector<T> &vec) {
    for (T &e : vec) std::cin >> e;
    return os;
}

template <typename T>
std::ostream &operator<<(std::ostream &os, const std::optional<T> &opt) {
    if (opt) {
        os << opt.value();
    } else {
        os << "invalid value";
    }
    return os;
}

void fast_io() {
    std::cout << std::fixed << std::setprecision(15);
    std::cin.tie(nullptr);
    std::ios::sync_with_stdio(false);
}

}  // namespace ebi
#line 2 "template/utility.hpp"

#line 5 "template/utility.hpp"

#line 2 "graph/base.hpp"

#line 7 "graph/base.hpp"

#line 2 "data_structure/simple_csr.hpp"

#line 6 "data_structure/simple_csr.hpp"

namespace ebi {

template <class E> struct simple_csr {
    simple_csr() = default;

    simple_csr(int n, const std::vector<std::pair<int, E>>& elements)
        : start(n + 1, 0), elist(elements.size()) {
        for (auto e : elements) {
            start[e.first + 1]++;
        }
        for (auto i : std::views::iota(0, n)) {
            start[i + 1] += start[i];
        }
        auto counter = start;
        for (auto [i, e] : elements) {
            elist[counter[i]++] = e;
        }
    }

    simple_csr(const std::vector<std::vector<E>>& es)
        : start(es.size() + 1, 0) {
        int n = es.size();
        for (auto i : std::views::iota(0, n)) {
            start[i + 1] = (int)es[i].size() + start[i];
        }
        elist.resize(start.back());
        for (auto i : std::views::iota(0, n)) {
            std::copy(es[i].begin(), es[i].end(), elist.begin() + start[i]);
        }
    }

    int size() const {
        return (int)start.size() - 1;
    }

    const auto operator[](int i) const {
        return std::ranges::subrange(elist.begin() + start[i],
                                     elist.begin() + start[i + 1]);
    }
    auto operator[](int i) {
        return std::ranges::subrange(elist.begin() + start[i],
                                     elist.begin() + start[i + 1]);
    }

    const auto operator()(int i, int l, int r) const {
        return std::ranges::subrange(elist.begin() + start[i] + l,
                                     elist.begin() + start[i + 1] + r);
    }
    auto operator()(int i, int l, int r) {
        return std::ranges::subrange(elist.begin() + start[i] + l,
                                     elist.begin() + start[i + 1] + r);
    }

  private:
    std::vector<int> start;
    std::vector<E> elist;
};

}  // namespace ebi
#line 9 "graph/base.hpp"

namespace ebi {

template <class T> struct Edge {
    int from, to;
    T cost;
    int id;
};

template <class E> struct Graph {
    using cost_type = E;
    using edge_type = Edge<cost_type>;

    Graph(int n_) : n(n_) {}

    Graph() = default;

    void add_edge(int u, int v, cost_type c) {
        assert(!prepared && u < n && v < n);
        buff.emplace_back(u, edge_type{u, v, c, m});
        edges.emplace_back(edge_type{u, v, c, m++});
    }

    void add_undirected_edge(int u, int v, cost_type c) {
        assert(!prepared && u < n && v < n);
        buff.emplace_back(u, edge_type{u, v, c, m});
        buff.emplace_back(v, edge_type{v, u, c, m});
        edges.emplace_back(edge_type{u, v, c, m});
        m++;
    }

    void read_tree(int offset = 1, bool is_weighted = false) {
        read_graph(n - 1, offset, false, is_weighted);
    }

    void read_parents(int offset = 1) {
        for (auto i : std::views::iota(1, n)) {
            int p;
            std::cin >> p;
            p -= offset;
            add_undirected_edge(p, i, 1);
        }
        build();
    }

    void read_graph(int e, int offset = 1, bool is_directed = false,
                    bool is_weighted = false) {
        for (int i = 0; i < e; i++) {
            int u, v;
            std::cin >> u >> v;
            u -= offset;
            v -= offset;
            if (is_weighted) {
                cost_type c;
                std::cin >> c;
                if (is_directed) {
                    add_edge(u, v, c);
                } else {
                    add_undirected_edge(u, v, c);
                }
            } else {
                if (is_directed) {
                    add_edge(u, v, 1);
                } else {
                    add_undirected_edge(u, v, 1);
                }
            }
        }
        build();
    }

    void build() {
        assert(!prepared);
        csr = simple_csr<edge_type>(n, buff);
        buff.clear();
        prepared = true;
    }

    int size() const {
        return n;
    }

    int node_number() const {
        return n;
    }

    int edge_number() const {
        return m;
    }

    edge_type get_edge(int i) const {
        assert(prepared);
        return edges[i];
    }

    std::vector<edge_type> get_edges() const {
        assert(prepared);
        return edges;
    }

    const auto operator[](int i) const {
        assert(prepared);
        return csr[i];
    }
    auto operator[](int i) {
        assert(prepared);
        return csr[i];
    }

  private:
    int n, m = 0;

    std::vector<std::pair<int, edge_type>> buff;

    std::vector<edge_type> edges;
    simple_csr<edge_type> csr;
    bool prepared = false;
};

}  // namespace ebi
#line 8 "template/utility.hpp"

namespace ebi {

template <class T> inline bool chmin(T &a, T b) {
    if (a > b) {
        a = b;
        return true;
    }
    return false;
}

template <class T> inline bool chmax(T &a, T b) {
    if (a < b) {
        a = b;
        return true;
    }
    return false;
}

template <class T> T safe_ceil(T a, T b) {
    if (a % b == 0)
        return a / b;
    else if (a >= 0)
        return (a / b) + 1;
    else
        return -((-a) / b);
}

template <class T> T safe_floor(T a, T b) {
    if (a % b == 0)
        return a / b;
    else if (a >= 0)
        return a / b;
    else
        return -((-a) / b) - 1;
}

constexpr i64 LNF = std::numeric_limits<i64>::max() / 4;

constexpr int INF = std::numeric_limits<int>::max() / 2;

const std::vector<int> dy = {1, 0, -1, 0, 1, 1, -1, -1};
const std::vector<int> dx = {0, 1, 0, -1, 1, -1, 1, -1};

}  // namespace ebi
#line 2 "tree/common_interval_decomposition_tree.hpp"

#line 7 "tree/common_interval_decomposition_tree.hpp"

#line 2 "data_structure/sparse_table.hpp"

#line 4 "data_structure/sparse_table.hpp"

/*
    reference: https://scrapbox.io/data-structures/Sparse_Table
*/

namespace ebi {

template <class Band, Band (*op)(Band, Band)> struct sparse_table {
  public:
    sparse_table() = default;

    sparse_table(const std::vector<Band> &a) : n(a.size()) {
        table = std::vector(std::__lg(n) + 1, std::vector<Band>(n));
        for (int i = 0; i < n; i++) {
            table[0][i] = a[i];
        }
        for (int k = 1; (1 << k) <= n; k++) {
            for (int i = 0; i + (1 << k) <= n; i++) {
                table[k][i] =
                    op(table[k - 1][i], table[k - 1][i + (1 << (k - 1))]);
            }
        }
    }

    void build(const std::vector<Band> &a) {
        n = (int)a.size();
        table = std::vector(std::__lg(n) + 1, std::vector<Band>(n));
        for (int i = 0; i < n; i++) {
            table[0][i] = a[i];
        }
        for (int k = 1; (1 << k) <= n; k++) {
            for (int i = 0; i + (1 << k) <= n; i++) {
                table[k][i] =
                    op(table[k - 1][i], table[k - 1][i + (1 << (k - 1))]);
            }
        }
    }

    // [l, r)

    Band fold(int l, int r) {
        int k = std::__lg(r - l);
        return op(table[k][l], table[k][r - (1 << k)]);
    }

  private:
    int n;
    std::vector<std::vector<Band>> table;
};

}  // namespace ebi
#line 9 "tree/common_interval_decomposition_tree.hpp"

/*
reference: https://www.mathenachia.blog/permutation-tree/
*/

namespace ebi {

struct common_interval_decomposition_tree {
  public:
    enum NodeType {
        Prime,
        Inc,
        Dec,
        One,
    };

    struct Node {
        int parent;
        NodeType type;
        int l, r;
        std::vector<int> child;

        bool is_prime() const {
            return type == Prime;
        }

        bool is_linear() const {
            return type != Prime;
        }

        bool is_leaf() const {
            return type == One;
        }
    };

  private:
    static int op(int a, int b) {
        return a < b ? a : b;
    }

    void build(const std::vector<int> &p) {
        int n = (int)p.size();
        std::vector<int> q(n, -1);
        for (int i = 0; i < n; i++) {
            assert(0 <= p[i] && p[i] < n && q[p[i]] == -1);
            q[p[i]] = i;
        }
        sparse_table<int, op> static_range_min(q);
        struct LeftBase {
            int l;
            int vl, vr;
        };
        struct Common {
            int l, r, v;
        };
        std::vector<LeftBase> stack;
        std::vector<Common> commons;
        for (int r = 1; r <= n; r++) {
            int a = p[r - 1];
            LeftBase y = {r - 1, a, a + 1};
            while (!stack.empty()) {
                if (y.vl < stack.back().vl) stack.back().vl = y.vl;
                if (y.vr > stack.back().vr) stack.back().vr = y.vr;
                auto x = stack.back();
                if (static_range_min.fold(x.vl, x.vr) < x.l) {
                    stack.pop_back();
                    auto &new_x = stack.back();
                    if (x.vl < new_x.vl) new_x.vl = x.vl;
                    if (x.vr > new_x.vr) new_x.vr = x.vr;
                } else if (x.vr - x.vl == r - x.l) {
                    y = x;
                    stack.pop_back();
                    commons.emplace_back(x.l, r, x.vl);
                } else {
                    break;
                }
            }
            stack.push_back(y);
        }
        while (stack.size() >= 2) {
            auto x = stack.back();
            stack.pop_back();
            auto &new_x = stack.back();
            if (x.vl < new_x.vl) new_x.vl = x.vl;
            if (x.vr > new_x.vr) new_x.vr = x.vr;
            if (new_x.vr - new_x.vl == n - new_x.l) {
                commons.emplace_back(new_x.l, n, new_x.vl);
            }
        }
        assert(stack.size() == 1);
        for (int i = 0; i < n; i++) tree.emplace_back(-1, One, i, i + 1);
        std::vector<int> id(n);
        std::iota(id.begin(), id.end(), 0);
        std::vector<int> right_list(n);
        std::iota(right_list.begin(), right_list.end(), 1);
        for (auto common : commons) {
            int m = right_list[common.l];
            if (right_list[m] == common.r) {
                int a = id[common.l];
                int b = id[m];
                right_list[common.l] = common.r;
                auto t = p[common.l] < p[common.r - 1] ? Inc : Dec;
                if (tree[a].type == t) {
                    tree[b].parent = a;
                    tree[a].r = common.r;
                    tree[a].child.push_back(b);
                } else {
                    int c = (int)tree.size();
                    tree.emplace_back(-1, t, common.l, common.r,
                                      std::vector<int>{a, b});
                    tree[a].parent = c;
                    tree[b].parent = c;
                    id[common.l] = c;
                }
            } else {
                int c = (int)tree.size();
                tree.emplace_back(-1, Prime, common.l, common.r);
                for (int i = common.l; i < common.r; i = right_list[i]) {
                    tree[id[i]].parent = c;
                    tree.back().child.push_back(id[i]);
                }
                id[common.l] = c;
                right_list[common.l] = common.r;
            }
        }
        root = id[0];
    }

  public:
    common_interval_decomposition_tree(const std::vector<int> &p) {
        build(p);
    }

    std::vector<Node> get_tree() const {
        return tree;
    }

    int root_id() const {
        return root;
    }

    Node get_node(int i) const {
        assert(0 <= i && i < (int)tree.size());
        return tree[i];
    }

    std::int64_t count_connected_interval() const {
        std::int64_t count = 0;
        for (const auto &node : tree) {
            if (node.type == Inc || node.type == Dec) {
                std::int64_t len = (int)node.child.size();
                count += len * (len - 1) / 2;
            } else {
                count++;
            }
        }
        return count;
    }

  private:
    int root;
    std::vector<Node> tree;
};

}  // namespace ebi
#line 8 "test/yuki/yuki_1720.test.cpp"

namespace ebi {

using mint = modint998244353;

void main_() {
    int n, k;
    std::cin >> n >> k;
    std::vector<int> p(n);
    std::cin >> p;
    rep(i, 0, n) p[i]--;
    Binomial<mint> binom(n);
    common_interval_decomposition_tree permutation_tree(p);
    auto dfs = [&](auto &&self, int v) -> std::vector<mint> {
        auto node = permutation_tree.get_node(v);
        if (node.is_leaf()) {
            std::vector<mint> ret(k + 1, 0);
            ret[1] = 1;
            return ret;
        }
        std::vector<mint> ret(k + 1, 0), prev(k + 1, 0), sum(k + 1, 0);
        ret[0] = 1;
        prev[0] = 1;
        for (auto ch : node.child) {
            ret = convolution_naive(ret, self(self, ch));
            ret.resize(k + 1);
            if (node.is_linear()) {
                rep(i, 0, k) {
                    ret[i + 1] += sum[i];
                }
            }
            rep(i,0,k) {
                sum[i] += prev[i];
            }
            prev = ret;
        }
        ret.resize(k + 1);
        if (node.is_prime()) ret[1]++;
        return ret;
    };
    auto ans = dfs(dfs, permutation_tree.root_id());
    ans.resize(k + 1);
    rep(i, 1, k + 1) {
        std::cout << ans[i] << '\n';
    }
}

}  // namespace ebi

int main() {
    ebi::fast_io();
    int t = 1;
    // std::cin >> t;
    while (t--) {
        ebi::main_();
    }
    return 0;
}

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