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:heavy_check_mark: test/aoj/aoj_3361.test.cpp

Depends on

Code

#define PROBLEM "https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=3361"

#include <cassert>
#include <iostream>
#include <vector>

#include "../../fps/fps_sparse.hpp"
#include "../../math/binomial.hpp"
#include "../../modint/modint.hpp"

using mint = ebi::modint998244353;

int main() {
    int k, n;
    std::vector<mint> f(300);
    ebi::Binomial<mint> comb(1000000);
    f[1] = 1;
    f[256] = -256;
    f[257] = 255;
    while (std::cin >> k >> n, !(n == 0 && k == 0)) {
        auto dp = ebi::pow_sparse(f, k, n + 1);
        assert(int(dp.size()) == n + 1);
        mint ans = 0;
        for (int i = n; i >= 0; i--) {
            ans += dp[i] * comb.c(2 * k - 1 + n - i, n - i);
        }
        std::cout << ans.val() << '\n';
    }
}
#line 1 "test/aoj/aoj_3361.test.cpp"
#define PROBLEM "https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=3361"

#include <cassert>
#include <iostream>
#include <vector>

#line 2 "fps/fps_sparse.hpp"

#line 5 "fps/fps_sparse.hpp"

#line 2 "math/mod_inv.hpp"

#line 5 "math/mod_inv.hpp"

#line 2 "modint/base.hpp"

#include <concepts>
#line 5 "modint/base.hpp"
#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 7 "math/mod_inv.hpp"

namespace ebi {

template <Modint mint> mint inv(int n) {
    static const int mod = mint::mod();
    static std::vector<mint> dat = {0, 1};
    assert(0 <= n);
    if (n >= mod) n -= mod;
    while (int(dat.size()) <= n) {
        int num = dat.size();
        int q = (mod + num - 1) / num;
        dat.emplace_back(dat[num * q - mod] * mint(q));
    }
    return dat[n];
}

}  // namespace ebi
#line 8 "fps/fps_sparse.hpp"

namespace ebi {

template <Modint mint>
std::vector<mint> mul_sparse(const std::vector<mint> &f,
                             const std::vector<mint> &g) {
    int n = f.size();
    int m = g.size();
    std::vector<std::pair<int, mint>> cf, cg;
    for (int i = 0; i < n; i++) {
        if (f[i] != 0) cf.emplace_back(i, f[i]);
    }
    for (int i = 0; i < m; i++) {
        if (g[i] != 0) cg.emplace_back(i, g[i]);
    }
    std::vector<mint> h(n + m - 1);
    for (auto [i, p] : cf) {
        for (auto [j, q] : cg) {
            h[i + j] += p * q;
        }
    }
    return h;
}

template <Modint mint>
std::vector<mint> inv_sparse(const std::vector<mint> &f, int d = -1) {
    assert(f[0] != 0);
    if (d < 0) {
        d = f.size();
    }
    std::vector<std::pair<int, mint>> ret;
    for (int i = 1; i < int(f.size()); i++) {
        if (f[i] != 0) {
            ret.emplace_back(i, f[i]);
        }
    }
    std::vector<mint> g(d);
    g[0] = f[0].inv();
    for (int i = 1; i < d; i++) {
        for (auto [k, p] : ret) {
            if (i - k < 0) break;
            g[i] -= g[i - k] * p;
        }
        g[i] *= g[0];
    }
    return g;
}

template <Modint mint>
std::vector<mint> exp_sparse(const std::vector<mint> &f, int d = -1) {
    int n = f.size();
    if (d < 0) d = n;
    std::vector<std::pair<int, mint>> ret;
    for (int i = 1; i < n; i++) {
        if (f[i] != 0) {
            ret.emplace_back(i - 1, f[i] * i);
        }
    }
    std::vector<mint> g(d);
    g[0] = 1;
    for (int i = 0; i < d - 1; i++) {
        for (auto [k, p] : ret) {
            if (i - k < 0) break;
            g[i + 1] += g[i - k] * p;
        }
        g[i + 1] *= inv<mint>(i + 1);
    }
    return g;
}

template <Modint mint>
std::vector<mint> log_sparse(const std::vector<mint> &f, int d = -1) {
    int n = f.size();
    if (d < 0) d = n;
    std::vector<mint> df(d);
    for (int i = 0; i < std::min(d, n - 1); i++) {
        df[i] = f[i + 1] * (i + 1);
    }
    auto dg = mul_sparse(df, inv_sparse(f));
    dg.resize(d);
    std::vector<mint> g(d);
    for (int i = 0; i < d - 1; i++) {
        g[i + 1] = dg[i] * inv<mint>(i + 1);
    }
    return g;
}

template <Modint mint>
std::vector<mint> pow_sparse_1(const std::vector<mint> &f, long long k,
                               int d = -1) {
    int n = f.size();
    assert(n == 0 || f[0] == 1);
    std::vector<std::pair<int, mint>> ret;
    for (int i = 1; i < n; i++) {
        if (f[i] != 0) ret.emplace_back(i, f[i]);
    }
    std::vector<mint> g(d);
    g[0] = 1;
    for (int i = 0; i < d - 1; i++) {
        for (const auto &[j, cf] : ret) {
            if (i + 1 - j < 0) break;
            g[i + 1] +=
                (mint(k) * mint(j) - mint(i - j + 1)) * cf * g[i + 1 - j];
        }
        g[i + 1] *= inv<mint>(i + 1);
    }
    return g;
}

template <Modint mint>
std::vector<mint> pow_sparse(const std::vector<mint> &f, long long k,
                             int d = -1) {
    int n = f.size();
    if (d < 0) d = n;
    assert(k >= 0);
    if (k == 0) {
        std::vector<mint> g(d);
        if (d > 0) g[0] = 1;
        return g;
    }
    for (int i = 0; i < n; i++) {
        if (f[i] != 0) {
            mint rev = f[i].inv();
            std::vector<mint> f2(n - i);
            for (int j = i; j < n; j++) {
                f2[j - i] = f[j] * rev;
            }
            f2 = pow_sparse_1(f2, k, d);
            mint fk = f[i].pow(k);
            std::vector<mint> g(d);
            for (int j = 0; j < int(f2.size()); j++) {
                if (j + i * k >= d) break;
                g[j + i * k] = f2[j] * fk;
            }
            return g;
        }
        if (i >= (d + k - 1) / k) break;
    }
    return std::vector<mint>(d);
}

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

#include <bit>
#line 6 "math/binomial.hpp"
#include <ranges>
#line 8 "math/binomial.hpp"

#line 10 "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 p(int n, int r) {
        if (r < 0 || n < r) return 0;
        return f(n) * inv_f(n - r);
    }

    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) {}

    constexpr static_modint(long long v) {
        v %= (long long)umod();
        if (v < 0) v += (long long)umod();
        _v = (unsigned int)v;
    }

    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 10 "test/aoj/aoj_3361.test.cpp"

using mint = ebi::modint998244353;

int main() {
    int k, n;
    std::vector<mint> f(300);
    ebi::Binomial<mint> comb(1000000);
    f[1] = 1;
    f[256] = -256;
    f[257] = 255;
    while (std::cin >> k >> n, !(n == 0 && k == 0)) {
        auto dp = ebi::pow_sparse(f, k, n + 1);
        assert(int(dp.size()) == n + 1);
        mint ans = 0;
        for (int i = n; i >= 0; i--) {
            ans += dp[i] * comb.c(2 * k - 1 + n - i, n - i);
        }
        std::cout << ans.val() << '\n';
    }
}
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