test/convolution/Convolution_Mod_1000000007.test.cpp

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• Last update: 2024-07-18 19:26:24+09:00
• Problem: https://judge.yosupo.jp/problem/convolution_mod_1000000007

Depends on

• Arbitrary Convolution (convolution/arbitrary_convolution.hpp)
• Convolution (convolution/convolution.hpp)
• NTT (convolution/ntt.hpp)
• math/internal_math.hpp
• modint/base.hpp
• modint/modint.hpp
• template/int_alias.hpp

Code

#define PROBLEM "https://judge.yosupo.jp/problem/convolution_mod_1000000007"

#include <iostream>
#include <vector>

#include "../../convolution/arbitrary_convolution.hpp"
#include "../../modint/modint.hpp"

using mint = ebi::modint1000000007;

int main() {
    int n, m;
    std::cin >> n >> m;
    std::vector<mint> a(n), b(m);
    for (int i = 0; i < n; i++) std::cin >> a[i];
    for (int i = 0; i < m; i++) std::cin >> b[i];
    auto c = ebi::arbitary_convolution<mint>(a, b);
    for (int i = 0; i < n + m - 1; i++) {
        std::cout << c[i].val() << " \n"[i == n + m - 2];
    }
}

#line 1 "test/convolution/Convolution_Mod_1000000007.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/convolution_mod_1000000007"

#include <iostream>
#include <vector>

#line 2 "convolution/arbitrary_convolution.hpp"

#include <cstdint>
#line 5 "convolution/arbitrary_convolution.hpp"

#line 2 "convolution/convolution.hpp"

#include <algorithm>
#include <bit>
#line 6 "convolution/convolution.hpp"

#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>
#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 2 "template/int_alias.hpp"

#line 4 "template/int_alias.hpp"

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 "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 9 "convolution/arbitrary_convolution.hpp"

namespace ebi {

namespace internal {

template <class T, Modint mint>
std::vector<mint> multiply(const std::vector<T>& f, const std::vector<T>& g) {
    std::vector<mint> a, b;
    a.reserve(f.size());
    b.reserve(g.size());
    for (auto x : f) a.emplace_back(x.val());
    for (auto x : g) b.emplace_back(x.val());
    return convolution<mint>(a, b);
}

}  // namespace internal

template <Modint mint>
std::vector<mint> arbitary_convolution(const std::vector<mint>& f,
                                       const std::vector<mint>& g) {
    if (f.empty() || g.empty()) return {};
    using i32 = std::int32_t;
    using i64 = std::int64_t;
    static constexpr i32 m0 = 167772161;  // 2^25
    static constexpr i32 m1 = 469762049;  // 2^26
    static constexpr i32 m2 = 754974721;  // 2^24
    using mint0 = static_modint<m0>;
    using mint1 = static_modint<m1>;
    using mint2 = static_modint<m2>;
    static constexpr i32 inv01 = mint1(m0).inv().val();
    static constexpr i32 inv02 = mint2(m0).inv().val();
    static constexpr i32 inv12 = mint2(m1).inv().val();
    static constexpr i32 inv02inv12 = i64(inv02) * inv12 % m2;
    static constexpr i64 w1 = m0;
    static constexpr i64 w2 = i64(m0) * m1;

    const i32 mod = mint::mod();

    auto d0 = internal::multiply<mint, mint0>(f, g);
    auto d1 = internal::multiply<mint, mint1>(f, g);
    auto d2 = internal::multiply<mint, mint2>(f, g);

    int n = d0.size();
    std::vector<mint> res(n);
    const int W1 = w1 % mod;
    const int W2 = w2 % mod;

    for (int i = 0; i < n; i++) {
        i32 n1 = d1[i].val(), n2 = d2[i].val(), a = d0[i].val();
        i32 b = i64(n1 + m1 - a) * inv01 % m1;
        i32 c = (i64(n2 + m2 - a) * inv02inv12 + i64(m2 - b) * inv12) % m2;
        res[i] = (i64(a) + i64(b) * W1 + i64(c) * W2) % mod;
    }
    return res;
}

}  // namespace ebi
#line 8 "test/convolution/Convolution_Mod_1000000007.test.cpp"

using mint = ebi::modint1000000007;

int main() {
    int n, m;
    std::cin >> n >> m;
    std::vector<mint> a(n), b(m);
    for (int i = 0; i < n; i++) std::cin >> a[i];
    for (int i = 0; i < m; i++) std::cin >> b[i];
    auto c = ebi::arbitary_convolution<mint>(a, b);
    for (int i = 0; i < n + m - 1; i++) {
        std::cout << c[i].val() << " \n"[i == n + m - 2];
    }
}

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