結果

問題 No.2413 Multiple of 99
ユーザー square1001
提出日時 2023-08-11 22:30:10
言語 C++17(gcc12)
(gcc 12.3.0 + boost 1.87.0)
結果
AC  
実行時間 6,756 ms / 8,000 ms
コード長 3,426 bytes
コンパイル時間 2,903 ms
コンパイル使用メモリ 111,780 KB
最終ジャッジ日時 2025-02-16 01:46:04
ジャッジサーバーID
（参考情報） 		judge5 / judge4
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 21
権限があれば一括ダウンロードができます

ソースコード

diff #
プレゼンテーションモードにする

#ifndef CLASS_MODINT
#define CLASS_MODINT
#include <cstdint>
template <std::uint32_t mod>
class modint {
private:
    std::uint32_t n;
public:
    modint() : n(0) {};
    modint(std::int64_t n_) : n((n_ >= 0 ? n_ : mod - (-n_) % mod) % mod) {};
    static constexpr std::uint32_t get_mod() { return mod; }
    std::uint32_t get() const { return n; }
    bool operator==(const modint& m) const { return n == m.n; }
    bool operator!=(const modint& m) const { return n != m.n; }
    modint& operator+=(const modint& m) { n += m.n; n = (n < mod ? n : n - mod); return *this; }
    modint& operator-=(const modint& m) { n += mod - m.n; n = (n < mod ? n : n - mod); return *this; }
    modint& operator*=(const modint& m) { n = std::uint64_t(n) * m.n % mod; return *this; }
    modint operator+(const modint& m) const { return modint(*this) += m; }
    modint operator-(const modint& m) const { return modint(*this) -= m; }
    modint operator*(const modint& m) const { return modint(*this) *= m; }
    modint inv() const { return (*this).pow(mod - 2); }
    modint pow(std::uint64_t b) const {
        modint ans = 1, m = modint(*this);
        while (b) {
            if (b & 1) ans *= m;
            m *= m;
            b >>= 1;
        }
        return ans;
    }
};
#endif // CLASS_MODINT
#include <vector>
#include <iostream>
#include <algorithm>
using namespace std;
using mint = modint<998244353>;
vector<mint> fft(int n, const vector<mint>& v, bool inv) {
    if (n == 1) {
        return v;
    }
    vector<mint> v0(n / 2), v1(n / 2);
    for (int i = 0; i < n / 2; i++) {
        v0[i] = v[i * 2 + 0];
        v1[i] = v[i * 2 + 1];
    }
    v0 = fft(n / 2, v0, inv);
    v1 = fft(n / 2, v1, inv);
    mint p = mint(3).pow((mint::get_mod() - 1) / n);
    if (inv) {
        p = p.inv();
    }
    mint mult = 1;
    vector<mint> res(n);
    for (int i = 0; i < n / 2; i++) {
        res[i] = v0[i] + v1[i] * mult;
        res[i + n / 2] = v0[i] - v1[i] * mult;
        mult *= p;
    }
    return res;
}
vector<mint> convolve(const vector<mint>& v1, const vector<mint>& v2) {
    if (v1.empty() || v2.empty()) {
        return vector<mint>();
    }
    int s = v1.size() + v2.size() - 1;
    int n = 1;
    while (n < s) {
        n *= 2;
    }
    vector<mint> c1 = v1, c2 = v2;
    c1.resize(n);
    c2.resize(n);
    c1 = fft(n, c1, false);
    c2 = fft(n, c2, false);
    for (int i = 0; i < n; i++) {
        c1[i] *= c2[i];
    }
    c1 = fft(n, c1, true);
    c1.resize(s);
    mint mult = mint(n).inv();
    for (int i = 0; i < s; i++) {
        c1[i] *= mult;
    }
    return c1;
}
vector<mint> power(vector<mint> poly, int n) {
    vector<mint> res = { mint(1) };
    while (n >= 1) {
        if (n % 2 == 1) {
            res = convolve(res, poly);
        }
        poly = convolve(poly, poly);
        n /= 2;
    }
    return res;
}
int main() {
    int N, K;
    cin >> N >> K;
    vector<mint> pbase(10, mint(1));
    vector<mint> p1 = power(pbase, (N + 1) / 2);
    vector<mint> p2 = power(pbase, N / 2);
    vector<mint> answer(N * 9 + 1, mint(0));
    for (int i = 0; i < 99; i++) {
        int target = (99 - i) * 10 % 99;
        vector<mint> subp1((p1.size() + 98) / 99);
        vector<mint> subp2((p2.size() + 98) / 99);
        for (int j = i; j < p1.size(); j += 99) {
            subp1[j / 99] = p1[j];
        }
        for (int j = target; j < p2.size(); j += 99) {
            subp2[j / 99] = p2[j];
        }
        vector<mint> res = convolve(subp1, subp2);
        for (int j = 0; j < res.size(); j++) {
            if (res[j] != mint(0)) {
                answer[j * 99 + i + target] += res[j];
            }
        }
    }
    mint final_answer = 0;
    for (int i = 0; i <= N * 9; i++) {
        if (answer[i] != mint(0)) {
            final_answer += answer[i] * mint(i).pow(K);
        }
    }
    cout << final_answer.get() << endl;
    return 0;
}
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