結果
問題 | No.2487 Multiple of M |
ユーザー |
👑 ![]() |
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 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 3 |
other | AC * 53 |
ソースコード
#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;}