結果

問題 No.1956 猫の額
ユーザー suisensuisen
提出日時 2022-05-24 00:30:47
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
MLE  
実行時間 -
コード長 15,115 bytes
コンパイル時間 4,798 ms
コンパイル使用メモリ 179,012 KB
実行使用メモリ 19,428 KB
最終ジャッジ日時 2023-10-20 18:40:09
合計ジャッジ時間 27,649 ms
ジャッジサーバーID
（参考情報） 		judge13 / judge12
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 MLE -
testcase_01 -- -
testcase_02 -- -
testcase_03 -- -
testcase_04 -- -
testcase_05 -- -
testcase_06 -- -
testcase_07 -- -
testcase_08 -- -
testcase_09 -- -
testcase_10 -- -
testcase_11 -- -
testcase_12 -- -
testcase_13 -- -
testcase_14 -- -
testcase_15 -- -
testcase_16 -- -
testcase_17 -- -
testcase_18 -- -
testcase_19 -- -
testcase_20 -- -
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ソースコード

diff # 

#include <array>
#include <iostream>
#include <vector>

#include <atcoder/modint>
#include <atcoder/convolution>

using mint = atcoder::modint;

#include <algorithm>
#include <cassert>
#include <iostream>

#include <vector>

namespace suisen {
template <typename mint>
class inv_mods {
    public:
        inv_mods() {}
        inv_mods(int n) { ensure(n); }
        const mint& operator[](int i) const {
            ensure(i);
            return invs[i];
        }
        static void ensure(int n) {
            int sz = invs.size();
            if (sz < 2) invs = {0, 1}, sz = 2;
            if (sz < n + 1) {
                invs.resize(n + 1);
                for (int i = sz; i <= n; ++i) invs[i] = mint(mod - mod / i) * invs[mod % i];
            }
        }
    private:
        static std::vector<mint> invs;
        static constexpr int mod = mint::mod();
};
template <typename mint>
std::vector<mint> inv_mods<mint>::invs{};
}

namespace suisen {

template <typename mint>
using convolution_t = std::vector<mint> (*)(const std::vector<mint> &, const std::vector<mint> &);

template <typename mint>
class FPS : public std::vector<mint> {
    public:
        using std::vector<mint>::vector;

        FPS(const std::initializer_list<mint> l) : std::vector<mint>::vector(l) {}
        FPS(const std::vector<mint> &v) : std::vector<mint>::vector(v) {}
        FPS(std::vector<mint> &&v) : std::vector<mint>::vector(std::move(v)) {}

        static void set_multiplication(convolution_t<mint> multiplication) {
            FPS<mint>::mult = multiplication;
        }

        inline const mint  operator[](int n) const noexcept { return n <= deg() ? unsafe_get(n) : 0; }
        inline       mint& operator[](int n)       noexcept { ensure_deg(n); return unsafe_get(n); }

        inline int size() const noexcept { return std::vector<mint>::size(); }
        inline int deg()  const noexcept { return size() - 1; }
        inline int normalize() {
            while (this->size() and this->back() == 0) this->pop_back();
            return deg();
        }
        inline FPS& pre_inplace(int max_deg) noexcept {
            if (deg() > max_deg) this->resize(std::max(0, max_deg + 1));
            return *this;
        }
        inline FPS pre(int max_deg) const noexcept { return FPS(*this).pre_inplace(max_deg); }

        inline FPS operator+() const { return FPS(*this); }
        FPS operator-() const {
            FPS f(*this);
            for (auto &e : f) e = mint::mod() - e;
            return f;
        }
        inline FPS& operator++() { ++(*this)[0]; return *this; }
        inline FPS& operator--() { --(*this)[0]; return *this; }
        inline FPS& operator+=(const mint x) { (*this)[0] += x; return *this; }
        inline FPS& operator-=(const mint x) { (*this)[0] -= x; return *this; }
        FPS& operator+=(const FPS &g) {
            ensure_deg(g.deg());
            for (int i = 0; i <= g.deg(); ++i) unsafe_get(i) += g.unsafe_get(i);
            return *this;
        }
        FPS& operator-=(const FPS &g) {
            ensure_deg(g.deg());
            for (int i = 0; i <= g.deg(); ++i) unsafe_get(i) -= g.unsafe_get(i);
            return *this;
        }
        inline FPS& operator*=(const FPS  &g) { return *this = FPS<mint>::mult(*this, g); }
        inline FPS& operator*=(      FPS &&g) { return *this = FPS<mint>::mult(*this, g); }
        inline FPS& operator*=(const mint x) {
            for (auto &e : *this) e *= x;
            return *this;
        }
        FPS& operator/=(FPS &&g) {
            const int fd = normalize(), gd = g.normalize();
            assert(gd >= 0);
            if (fd < gd) { this->clear(); return *this; }
            if (gd == 0) return *this *= g.unsafe_get(0).inv();
            static constexpr int THRESHOLD_NAIVE_POLY_QUOTIENT = 256;
            if (gd <= THRESHOLD_NAIVE_POLY_QUOTIENT) {
                *this = std::move(naive_div_inplace(std::move(g), gd).first);
                return *this;
            }
            std::reverse(this->begin(), this->end()), std::reverse(g.begin(), g.end());
            const int k = fd - gd;
            *this *= g.inv_inplace(k), this->resize(k + 1);
            std::reverse(this->begin(), this->end());
            return *this;
        }
        FPS& operator%=(FPS &&g) {
            int fd = normalize(), gd = g.normalize();
            assert(gd >= 0);
            if (fd < gd) return *this;
            if (gd == 0) { this->clear(); return *this; }
            static constexpr int THRESHOLD_NAIVE_REMAINDER = 256;
            if (gd <= THRESHOLD_NAIVE_REMAINDER) return naive_div_inplace(std::move(g), gd).second;
            *this -= g * (*this / g);
            return pre_inplace(gd - 1);
        }
        inline FPS& operator/=(const FPS &g) { return *this /= FPS(g); }
        inline FPS& operator%=(const FPS &g) { return *this %= FPS(g); }
        FPS& operator<<=(const int shamt) {
            this->insert(this->begin(), shamt, 0);
            return *this;
        }
        FPS& operator>>=(const int shamt) {
            if (shamt > size()) this->clear();
            else this->erase(this->begin(), this->begin() + shamt);
            return *this;
        }

        inline FPS operator+(FPS &&g) const { return FPS(*this) += std::move(g); }
        inline FPS operator-(FPS &&g) const { return FPS(*this) -= std::move(g); }
        inline FPS operator*(FPS &&g) const { return FPS(*this) *= std::move(g); }
        inline FPS operator/(FPS &&g) const { return FPS(*this) /= std::move(g); }
        inline FPS operator%(FPS &&g) const { return FPS(*this) %= std::move(g); }
        inline FPS operator+(const FPS &g) const { return FPS(*this) += g; }
        inline FPS operator+(const mint x) const { return FPS(*this) += x; }
        inline FPS operator-(const FPS &g) const { return FPS(*this) -= g; }
        inline FPS operator-(const mint x) const { return FPS(*this) -= x; }
        inline FPS operator*(const FPS &g) const { return FPS(*this) *= g; }
        inline FPS operator*(const mint x) const { return FPS(*this) *= x; }
        inline FPS operator/(const FPS &g) const { return FPS(*this) /= g; }
        inline FPS operator%(const FPS &g) const { return FPS(*this) %= g; }
        inline friend FPS operator*(const mint x, const FPS  &f) { return f * x; }
        inline friend FPS operator*(const mint x,       FPS &&f) { return f *= x; }
        inline FPS operator<<(const int shamt) { return FPS(*this) <<= shamt; }
        inline FPS operator>>(const int shamt) { return FPS(*this) >>= shamt; }

        friend bool operator==(const FPS &f, const FPS &g) {
            int n = f.size(), m = g.size();
            if (n < m) return g == f;
            for (int i = 0; i < m; ++i) if (f.unsafe_get(i) != g.unsafe_get(i)) return false;
            for (int i = m; i < n; ++i) if (f.unsafe_get(i) != 0) return false;
            return true;
        }

        FPS& diff_inplace() {
            if (this->size() == 0) return *this;
            for (int i = 1; i <= deg(); ++i) unsafe_get(i - 1) = unsafe_get(i) * i;
            this->pop_back();
            return *this;
        }
        FPS& intg_inplace() {
            int d = deg();
            ensure_deg(d + 1);
            for (int i = d; i >= 0; --i) unsafe_get(i + 1) = unsafe_get(i) * invs[i + 1];
            unsafe_get(0) = 0;
            return *this;
        }
        FPS& inv_inplace(const int max_deg) {
            FPS res { unsafe_get(0).inv() };
            for (int k = 1; k <= max_deg; k *= 2) {
                FPS tmp(this->pre(k * 2) * (res * res));
                res *= 2, res -= tmp.pre_inplace(2 * k);
            }
            return *this = std::move(res), pre_inplace(max_deg);
        }
        FPS& log_inplace(const int max_deg) {
            FPS f_inv = inv(max_deg);
            diff_inplace(), *this *= f_inv, pre_inplace(max_deg - 1), intg_inplace();
            return *this;
        }
        FPS& exp_inplace(const int max_deg) {
            FPS res {1};
            for (int k = 1; k <= max_deg; k *= 2) res *= ++(pre(k * 2) - res.log(k * 2)), res.pre_inplace(k * 2);
            return *this = std::move(res), pre_inplace(max_deg);
        }
        FPS& pow_inplace(const long long k, const int max_deg) {
            int tlz = 0;
            while (tlz <= deg() and unsafe_get(tlz) == 0) ++tlz;
            if (tlz * k > max_deg) { this->clear(); return *this; }
            *this >>= tlz;
            mint base = (*this)[0];
            *this *= base.inv(), log_inplace(max_deg), *this *= k, exp_inplace(max_deg), *this *= base.pow(k);
            return *this <<= tlz * k, pre_inplace(max_deg);
        }
        inline FPS diff() const { return FPS(*this).diff_inplace(); }
        inline FPS intg() const { return FPS(*this).intg_inplace(); }
        inline FPS inv(const int max_deg) const { return FPS(*this).inv_inplace(max_deg); }
        inline FPS log(const int max_deg) const { return FPS(*this).log_inplace(max_deg); }
        inline FPS exp(const int max_deg) const { return FPS(*this).exp_inplace(max_deg); }
        inline FPS pow(const long long k, const int max_deg) const { return FPS(*this).pow_inplace(k, max_deg); }

        mint eval(mint x) const {
            mint y = 0;
            for (int i = size() - 1; i >= 0; --i) y = y * x + unsafe_get(i);
            return y;
        }

    private:
        static inline inv_mods<mint> invs;
        static convolution_t<mint> mult;
        inline void ensure_deg(int d) { if (deg() < d) this->resize(d + 1, 0); }
        inline const mint& unsafe_get(int i) const { return std::vector<mint>::operator[](i); }
        inline       mint& unsafe_get(int i)       { return std::vector<mint>::operator[](i); }

        std::pair<FPS, FPS&> naive_div_inplace(FPS &&g, const int gd) {
            const int k = deg() - gd;
            mint head_inv = g.unsafe_get(gd).inv();
            FPS q(k + 1);
            for (int i = k; i >= 0; --i) {
                mint div = this->unsafe_get(i + gd) * head_inv;
                q.unsafe_get(i) = div;
                for (int j = 0; j <= gd; ++j) this->unsafe_get(i + j) -= div * g.unsafe_get(j);
            }
            return {q, pre_inplace(gd - 1)};
        }
};

template <typename mint>
convolution_t<mint> FPS<mint>::mult = [](const auto &, const auto &) {
    std::cerr << "convolution function is not available." << std::endl;
    assert(false);
    return std::vector<mint>{};
};

} // namespace suisen

template <typename mint>
auto sqrt(suisen::FPS<mint> a) -> decltype(mint::mod(), suisen::FPS<mint>{})  {
    assert(false);
}
template <typename mint>
auto log(suisen::FPS<mint> a) -> decltype(mint::mod(), suisen::FPS<mint>{}) {
    return a.log(a.deg());
}
template <typename mint>
auto exp(suisen::FPS<mint> a) -> decltype(mint::mod(), mint()) {
    return a.exp(a.deg());
}
template <typename mint, typename T>
auto pow(suisen::FPS<mint> a, T b) -> decltype(mint::mod(), mint()) {
    return a.pow(b, a.deg());
}
template <typename mint>
auto inv(suisen::FPS<mint> a) -> decltype(mint::mod(), suisen::FPS<mint>{})  {
    return a.inv(a.deg());
}

namespace suisen {
    template <typename mint>
    FPS<mint> polynomial_interpolation(const std::vector<mint>& xs, const std::vector<mint>& ys) {
        assert(xs.size() == ys.size());
        int n = xs.size();
        std::vector<FPS<mint>> seg(2 * n), g(2 * n);
        for (int i = 0; i < n; ++i) seg[n + i] = FPS<mint>{ -xs[i], 1 };
        for (int i = n - 1; i > 0; --i) {
            seg[i] = seg[i * 2] * seg[i * 2 + 1];
        }
        g[1] = std::move(seg[1].diff_inplace());
        for (int i = 1; i < n; ++i) {
            int l = 2 * i, r = l + 1;
            g[l] = g[i] % seg[l], g[r] = g[i] % seg[r];
        }
        for (int i = 0; i < n; ++i) g[n + i] = FPS<mint>{ ys[i] / g[n + i][0] };
        for (int i = n - 1; i > 0; --i) {
            int l = 2 * i, r = l + 1;
            g[i] = g[l] * seg[r] + g[r] * seg[l];
        }
        return g[1];
    }

} // namespace suisen

constexpr int N = 100000;

constexpr long long MOD1 = 1107296257;
constexpr long long MOD2 = 1711276033;
constexpr long long MOD3 = 1224736769;
constexpr long long M1M2 = MOD1 * MOD2;
constexpr long long INV_M1_MOD2 = atcoder::internal::inv_gcd(MOD1, MOD2).second;
constexpr long long INV_M1M2_MOD3 = atcoder::internal::inv_gcd(M1M2, MOD3).second;

using mint1 = atcoder::static_modint<MOD1>;
using mint2 = atcoder::static_modint<MOD2>;
using mint3 = atcoder::static_modint<MOD3>;

mint garner(mint1 c1, mint2 c2, mint3 c3) {
    const long long m1m2 = mint(M1M2).val();
    long long x1 = c1.val();
    long long x2 = (atcoder::static_modint<MOD2>(c2.val() - x1) * INV_M1_MOD2).val();
    long long x3 = (atcoder::static_modint<MOD3>(c3.val() - x1 - x2 * MOD1) * INV_M1M2_MOD3).val();
    return x1 + x2 * MOD1 + x3 * m1m2;
}

template <typename T>
std::vector<T> solve(int n, int c, int s, std::array<int, N + 1> cnt) {
    suisen::FPS<T>::set_multiplication([](const auto& a, const auto& b) { return atcoder::convolution(a, b); });

    std::vector<std::vector<T>> binom(n + 1);
    for (int i = 0; i <= n; ++i) {
        binom[i].resize(i + 1);
        binom[i][0] = binom[i][i] = 1;
        for (int j = 1; j < i; ++j) {
            binom[i][j] = binom[i - 1][j - 1] + binom[i - 1][j];
        }
    }

    std::vector<T> ans(s + 1);

    const int m1 = s / 4, m2 = m1 + s / 4, m3 = m2 + s / 4, m4 = s + 1;
    std::array<int, 5> sep{ 0, m1, m2, m3, s + 1 };

    for (int sep_i = 0; sep_i < 4; ++sep_i) {
        const int l = sep[sep_i], r = sep[sep_i + 1];

        std::vector<T> xs(n + 1);
        std::vector<std::vector<T>> ys(r - l, std::vector<T>(n + 1));

        for (int x = 0; x <= n; ++x) {
            xs[x] = x;

            std::vector<T> dp(s + 1);
            dp[0] = 1;
            for (int val = N; val >= 1; --val) if (const int p = cnt[val]; p != 0) {
                for (int sum = s; sum >= 0; --sum) {
                    const int max_num = std::min(p, sum / val);
                    T pow_x = 1;
                    for (int num = 1; num <= max_num; ++num) {
                        pow_x *= x;
                        dp[sum] += dp[sum - val * num] * binom[p][num] * pow_x;
                    }
                }
            }
            for (int sum = l; sum < r; ++sum) {
                ys[sum - l][x] = dp[sum];
            }
        }

        for (int sum = l; sum < r; ++sum) {
            ans[sum] = suisen::polynomial_interpolation(xs, ys[sum - l])[c];
        }
    }
    return ans;
}

int main() {
    int n, m, c;
    std::cin >> n >> m >> c;
    mint::set_mod(m);

    int s = 0;
    std::array<int, N + 1> cnt{};
    for (int i = 0; i < n; ++i) {
        int e;
        std::cin >> e;
        s += e;
        ++cnt[e];
    }

    auto ans1 = solve<mint1>(n, c, s, cnt);
    auto ans2 = solve<mint2>(n, c, s, cnt);
    auto ans3 = solve<mint3>(n, c, s, cnt);

    for (int sum = 1; sum <= s; ++sum) {
        std::cout << garner(ans1[sum], ans2[sum], ans3[sum]).val() << " \n"[s == sum];
    }

    return 0;
}
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