結果

問題 No.2487 Multiple of M
ユーザー 👑 NachiaNachia
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 #
プレゼンテーションモードにする

#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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