結果

問題 No.2487 Multiple of M
ユーザー 👑 Nachia
提出日時 2023-09-29 23:29:52
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 2 ms / 2,000 ms
コード長 4,783 bytes
コンパイル時間 949 ms
コンパイル使用メモリ 84,472 KB
最終ジャッジ日時 2025-02-17 03:36:23
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 * 53
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 # 

#line 1 "..\\Main.cpp"

#include <iostream>
#include <string>
#include <vector>
#include <numeric>
#include <algorithm>
#include <atcoder/modint>
#line 2 "D:\\Programming\\VSCode\\competitive-cpp\\nachia\\linear-modulo\\matrix-modulo.hpp"

#line 4 "D:\\Programming\\VSCode\\competitive-cpp\\nachia\\linear-modulo\\matrix-modulo.hpp"
#include <cassert>
#include <utility>


namespace nachia{

template<class Elem>
struct MatrixModulo{
private:
    int h;
    int w;
    std::vector<Elem> elems;

public:
    
    MatrixModulo(int new_h=0, int new_w=0){ h = new_h; w = new_w; elems.assign(h * w, 0); }
    MatrixModulo(const MatrixModulo &) = default;
    int numRow() const { return h; }
    int numColumn() const { return w; }
    int height() const { return numRow(); }
    int width() const { return numColumn(); }
    typename std::vector<Elem>::iterator operator[](int y){ return elems.begin() + (y * w); }
    typename std::vector<Elem>::const_iterator operator[](int y) const { return elems.begin() + (y * w); }
    static MatrixModulo Identity(int idx){ auto res = MatrixModulo(idx, idx); for(int i = 0; i < idx; i++) res[i][i] = 1; return res; }
    void swapColumns(int x1, int x2){
        assert(0 <= x1 && x1 < numColumn());
        assert(0 <= x2 && x2 < numColumn());
        for(int y=0; y<numRow(); y++) std::swap((*this)[y][x1], (*this)[y][x2]);
    }
    void swapRows(int y1, int y2){
        assert(0 <= y1 && y1 < numRow());
        assert(0 <= y2 && y2 < numRow());
        for(int x=0; x<numColumn(); x++) std::swap((*this)[y1][x], (*this)[y2][x]);
    }
    MatrixModulo operator*(const MatrixModulo& r) const {
        assert(width() == r.height());
        auto res = MatrixModulo(h, r.w);
        for (int i=0; i<h; i++) for (int j=0; j<w; j++) for (int k=0; k<r.w; k++) res[i][k] += (*this)[i][j] * r[j][k];
        return res;
    }
    Elem det() const {
        assert(height() == width());
        MatrixModulo g = *this;
        Elem ans = 1;
        for (int i=0; i<h; i++) {
            int tg = -1;
            for (int j=i; j<h; j++) { if (g[j][i].val() != 0) tg = j; }
            if (tg == -1) return 0;
            if (tg != i) ans = -ans;
            for (int j=0; j<h; j++) std::swap(g[i][j], g[tg][j]);
            tg = i;
            ans *= g[i][i];
            Elem const_coeff = g[i][i].inv();
            for (int j=0; j<h; j++) g[i][j] *= const_coeff;
            for (int j=i+1; j<h; j++) for(int k=h-1; k>=i; k--) g[j][k] -= g[j][i] * g[i][k];
        }
        return ans;
    }
    int rank() const {
        MatrixModulo g = *this;
        int y = 0;
        for (int d=0; d<w; d++) {
            if(y == h) break;
            int tg = -1;
            for (int i=y; i<h; i++) { if (g[i][d].val() != 0){ tg = i; break; } }
            if (tg == -1) continue;
            for (int j=d; j<w; j++) std::swap(g[y][j], g[tg][j]);
            tg = y;
            Elem const_coeff = g[y][d].inv();
            for (int j=d; j<w; j++) g[y][j] *= const_coeff;
            for (int i=y+1; i<h; i++) for(int j=w-1; j>=d; j--) g[i][j] -= g[i][d] * g[y][j];
            y++;
        }
        return y;
    }
    MatrixModulo pow(unsigned long long i){
        auto a = *this;
        auto res = Identity(height());
        while(i){
            if(i % 2 == 1) res = res * a;
            a = a * a;
            i /= 2;
        }
        return res;
    }
};


} // namespace nachia
#line 9 "..\\Main.cpp"
using Modint = atcoder::static_modint<998244353>;
using namespace std;
using i64 = long long;
using u64 = unsigned long long;
#define rep(i,n) for(int i=0; i<(int)(n); i++)
const i64 INF = 1001001001001001001;

pair<Modint, Modint> solve(i64 N, i64 M, i64 K, i64 Q = 1){
    if(N == 0) return { 1, 0 };
    i64 g = std::gcd(M, K);
    if(g == 1){
        auto mat = nachia::MatrixModulo<Modint>(2,2);
        mat[0][0] = Modint(Q-1);
        mat[0][1] = Modint(Q);
        mat[1][0] = Modint(M-1)*(Q);
        mat[1][1] = Modint(M-2)*(Q) + Modint(Q-1);
        mat = mat.pow(N);
     //   cout << "solve(" << N << ", " << M << ", " << K << ", " << Q << ") = ";
     //   cout << "(" << mat[0][0].val() << ", " << (mat[0][1] * (M-1)).val() << ")" << endl;
        return make_pair(mat[0][0], mat[0][1] * (M-1));
    }
    auto [c0, c1] = solve(N-1, M/g, K, Q*g);
    Modint a0 = (c1 * 1) * Q + c0 * (Q-1);
    Modint a1 = (c0 * (M-1) + c1 * (M - 2)) * Q + c1 * (Q-1);
  //  cout << "solve(" << N << ", " << M << ", " << K << ", " << Q << ") = ";
  //  cout << "(" << a0.val() << ", " << a1.val() << ")" << endl;
    return { a0, a1 };
}

void testcase(){
    i64 N, M, K; cin >> N >> M >> K;
    cout << solve(N,M,K).first.val() << endl;
}

int main(){
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    testcase();
    return 0;
}
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