結果

問題 No.2487 Multiple of M
ユーザー ecotteaecottea
提出日時 2023-09-30 00:24:24
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 13,690 bytes
コンパイル時間 3,503 ms
コンパイル使用メモリ 255,292 KB
最終ジャッジ日時 2025-02-17 03:43:34
ジャッジサーバーID
(参考情報)
judge5 / judge2
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

#ifndef HIDDEN_IN_VS //
//
#define _CRT_SECURE_NO_WARNINGS
//
#include <bits/stdc++.h>
using namespace std;
//
using ll = long long; // -2^63 2^63 = 9 * 10^18int -2^31 2^31 = 2 * 10^9
using pii = pair<int, int>; using pll = pair<ll, ll>; using pil = pair<int, ll>; using pli = pair<ll, int>;
using vi = vector<int>; using vvi = vector<vi>; using vvvi = vector<vvi>; using vvvvi = vector<vvvi>;
using vl = vector<ll>; using vvl = vector<vl>; using vvvl = vector<vvl>; using vvvvl = vector<vvvl>;
using vb = vector<bool>; using vvb = vector<vb>; using vvvb = vector<vvb>;
using vc = vector<char>; using vvc = vector<vc>; using vvvc = vector<vvc>;
using vd = vector<double>; using vvd = vector<vd>; using vvvd = vector<vvd>;
template <class T> using priority_queue_rev = priority_queue<T, vector<T>, greater<T>>;
using Graph = vvi;
//
const double PI = acos(-1);
const vi DX = { 1, 0, -1, 0 }; // 4
const vi DY = { 0, 1, 0, -1 };
int INF = 1001001001; ll INFL = 4004004003104004004LL; // (int)INFL = 1010931620;
double EPS = 1e-15;
//
struct fast_io { fast_io() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(18); } } fastIOtmp;
//
#define all(a) (a).begin(), (a).end()
#define sz(x) ((int)(x).size())
#define lbpos(a, x) (int)distance((a).begin(), std::lower_bound(all(a), x))
#define ubpos(a, x) (int)distance((a).begin(), std::upper_bound(all(a), x))
#define Yes(b) {cout << ((b) ? "Yes\n" : "No\n");}
#define rep(i, n) for(int i = 0, i##_len = int(n); i < i##_len; ++i) // 0 n-1
#define repi(i, s, t) for(int i = int(s), i##_end = int(t); i <= i##_end; ++i) // s t
#define repir(i, s, t) for(int i = int(s), i##_end = int(t); i >= i##_end; --i) // s t
#define repe(v, a) for(const auto& v : (a)) // a
#define repea(v, a) for(auto& v : (a)) // a
#define repb(set, d) for(int set = 0; set < (1 << int(d)); ++set) // d
#define repp(a) sort(all(a)); for(bool a##_perm = true; a##_perm; a##_perm = next_permutation(all(a))) // a
#define smod(n, m) ((((n) % (m)) + (m)) % (m)) // mod
#define uniq(a) {sort(all(a)); (a).erase(unique(all(a)), (a).end());} //
#define EXIT(a) {cout << (a) << endl; exit(0);} //
#define inQ(x, y, u, l, d, r) ((u) <= (x) && (l) <= (y) && (x) < (d) && (y) < (r)) //
//
template <class T> inline ll pow(T n, int k) { ll v = 1; rep(i, k) v *= n; return v; }
template <class T> inline bool chmax(T& M, const T& x) { if (M < x) { M = x; return true; } return false; } // true
    
template <class T> inline bool chmin(T& m, const T& x) { if (m > x) { m = x; return true; } return false; } // true
    
template <class T> inline T get(T set, int i) { return (set >> i) & T(1); }
//
template <class T, class U> inline istream& operator>>(istream& is, pair<T, U>& p) { is >> p.first >> p.second; return is; }
template <class T> inline istream& operator>>(istream& is, vector<T>& v) { repea(x, v) is >> x; return is; }
template <class T> inline vector<T>& operator--(vector<T>& v) { repea(x, v) --x; return v; }
template <class T> inline vector<T>& operator++(vector<T>& v) { repea(x, v) ++x; return v; }
#endif //
#if __has_include(<atcoder/all>)
#include <atcoder/all>
using namespace atcoder;
#ifdef _MSC_VER
#include "localACL.hpp"
#endif
//using mint = modint1000000007;
using mint = modint998244353;
//using mint = modint; // mint::set_mod(m);
namespace atcoder {
inline istream& operator>>(istream& is, mint& x) { ll x_; is >> x_; x = x_; return is; }
inline ostream& operator<<(ostream& os, const mint& x) { os << x.val(); return os; }
}
using vm = vector<mint>; using vvm = vector<vm>; using vvvm = vector<vvm>; using vvvvm = vector<vvvm>;
#endif
#ifdef _MSC_VER // Visual Studio
#include "local.hpp"
#else // gcc
inline int popcount(int n) { return __builtin_popcount(n); }
inline int popcount(ll n) { return __builtin_popcountll(n); }
inline int lsb(int n) { return n != 0 ? __builtin_ctz(n) : -1; }
inline int lsb(ll n) { return n != 0 ? __builtin_ctzll(n) : -1; }
inline int msb(int n) { return n != 0 ? (31 - __builtin_clz(n)) : -1; }
inline int msb(ll n) { return n != 0 ? (63 - __builtin_clzll(n)) : -1; }
inline int msb(__int128 n) { return (n >> 64) != 0 ? (127 - __builtin_clzll((ll)(n >> 64))) : n != 0 ? (63 - __builtin_clzll((ll)(n))) : -1; }
#define gcd __gcd
#define dump(...)
#define dumpel(v)
#define dump_list(v)
#define dump_mat(v)
#define input_from_file(f)
#define output_to_file(f)
#define Assert(b) { if (!(b)) while (1) cout << "OLE"; }
#endif
//32 bit
/*
* set_mod(ll m) : O(√m)
* m
*
*
* Divisible_mint(ll x = 1) : O(ω(m))ω(m) : m
* x
*
* x * y, x / y : O(ω(m))
* 使
*
* ll val() : O(ω(m))
* m -1
*
* ll gcd(ll x) : O(ω(m))
* x GCD
* x m
*/
class Divisible_mint {
// MOD :
static inline ll MOD;
// ps[i] : i K
static inline int K;
static inline vl ps;
// num : dnm : ps
ll num, dnm;
// es[i] : ps[i]
vl es;
// is_zero : 0
bool is_zero;
// m ps[0..K), es_max[0..K)
static void factor_integer(ll m) {
ps.clear();
// m ps
for (ll p = 2; p * p <= m; p++) {
if (m % p != 0) continue;
while (m % p == 0) m /= p;
ps.push_back(p);
}
if (m > 1) ps.push_back(m);
K = sz(ps);
}
// a, b a x + b y = 1 (x, y)
void extended_gcd(ll a, ll b, ll& x, ll& y) const {
if (b == 0) {
x = 1;
y = 0;
return;
}
ll q = a / b, r = a % b, X, Y;
extended_gcd(b, r, X, Y);
x = Y;
y = X - q * Y;
}
// a^n (mod MOD)
ll pow_mod(ll a, ll n) const {
ll res = 1, pow_a = a;
while (n > 0) {
if (n & 1) res = (res * pow_a) % MOD;
pow_a = (pow_a * pow_a) % MOD;
n /= 2;
}
return res;
}
public:
// m
static void set_mod(ll m) {
// verify : https://yukicoder.me/problems/no/2273
MOD = m;
factor_integer(m);
}
// x
Divisible_mint(ll x) : num(x), dnm(1), es(K), is_zero(false) {
// verify : https://yukicoder.me/problems/no/2273
if (x == 0) {
is_zero = true;
return;
}
rep(k, K) {
while (num % ps[k] == 0) {
es[k]++;
num /= ps[k];
}
}
num %= MOD;
if (num < 0) num += MOD;
}
// 1
Divisible_mint() : num(1), dnm(1), es(K), is_zero(false) {}
//
Divisible_mint& operator*=(const Divisible_mint& b) {
// verify : https://yukicoder.me/problems/no/2273
if (b.is_zero) {
is_zero = true;
return *this;
}
num = (num * b.num) % MOD;
dnm = (dnm * b.dnm) % MOD;
rep(k, K) es[k] += b.es[k];
return *this;
}
Divisible_mint& operator/=(const Divisible_mint& b) {
// verify : https://yukicoder.me/problems/no/2273
Assert(!b.is_zero);
num = (num * b.dnm) % MOD;
dnm = (dnm * b.num) % MOD;
rep(k, K) es[k] -= b.es[k];
return *this;
}
Divisible_mint operator*(const Divisible_mint& b) const { Divisible_mint a = *this; return a *= b; }
Divisible_mint operator/(const Divisible_mint& b) const { Divisible_mint a = *this; return a /= b; }
// m -1
ll val() const {
// verify : https://yukicoder.me/problems/no/2273
if (is_zero) return 0;
//
ll dnm_inv, tmp;
extended_gcd(dnm, MOD, dnm_inv, tmp);
ll res = (num * dnm_inv) % MOD;
if (res < 0) res += MOD;
// ps[0..K)
rep(k, K) {
if (es[k] < 0) return -1;
res = (res * pow_mod(ps[k], es[k])) % MOD;
}
return res;
}
// x GCD
ll gcd(ll x) const {
// verify : https://yukicoder.me/problems/no/2273
ll res = 1;
rep(k, K) {
ll e = 0;
while (x % ps[k] == 0) {
e++;
x /= ps[k];
}
rep(hoge, min(es[k], e)) res *= ps[k];
}
return res;
}
// m
Divisible_mint pow(ll m) {
if (is_zero) return *this;
auto res(*this);
res.num = pow_mod(num, m);
res.dnm = pow_mod(dnm, m);
rep(k, K) res.es[k] *= m;
return res;
}
#ifdef _MSC_VER
friend ostream& operator<<(ostream& os, Divisible_mint DM) {
os << DM.val();
return os;
}
#endif
};
//
/*
* Fixed_matrix<T, n>() : O(n^2)
* T n×n
*
* Fixed_matrix<T, n>(bool identity = true) : O(n^2)
* T n×n
*
* Fixed_matrix<T, n>(vvT a) : O(n^2)
* a[0..n)[0..n)
*
* A + B : O(n^2)
* n×n A, B += 使
*
* A - B : O(n^2)
* n×n A, B -= 使
*
* c * A A * c : O(n^2)
* n×n A c *= 使
*
* A * x : O(n^2)
* n×n A n array<T, n> x
*
* x * A : O(n^2)
* n array<T, n> x n×n A
*
* A * B : O(n^3)
* n×n A n×n B
*
* Mat pow(ll d) : O(n^3 log d)
* d
*/
template <class T, int n>
struct Fixed_matrix {
array<array<T, n>, n> v; //
// n×n identity = true n×n
Fixed_matrix(bool identity = false) {
rep(i, n) v[i].fill(T(0));
if (identity) rep(i, n) v[i][i] = T(1);
}
// a[0..n)[0..n)
Fixed_matrix(const vector<vector<T>>& a) {
// verify : https://yukicoder.me/problems/no/1000
Assert(sz(a) == n && sz(a[0]) == n);
rep(i, n) rep(j, n) v[i][j] = a[i][j];
}
//
Fixed_matrix(const Fixed_matrix&) = default;
Fixed_matrix& operator=(const Fixed_matrix&) = default;
//
inline array<T, n> const& operator[](int i) const { return v[i]; }
inline array<T, n>& operator[](int i) { return v[i]; }
//
friend istream& operator>>(istream& is, Fixed_matrix& a) {
rep(i, n) rep(j, n) is >> a[i][j];
return is;
}
//
bool operator==(const Fixed_matrix& b) const { return v == b.v; }
bool operator!=(const Fixed_matrix& b) const { return !(*this == b); }
//
Fixed_matrix& operator+=(const Fixed_matrix& b) {
rep(i, n) rep(j, n) v[i][j] += b[i][j];
return *this;
}
Fixed_matrix& operator-=(const Fixed_matrix& b) {
rep(i, n) rep(j, n) v[i][j] -= b[i][j];
return *this;
}
Fixed_matrix& operator*=(const T& c) {
rep(i, n) rep(j, n) v[i][j] *= c;
return *this;
}
Fixed_matrix operator+(const Fixed_matrix& b) const { return Fixed_matrix(*this) += b; }
Fixed_matrix operator-(const Fixed_matrix& b) const { return Fixed_matrix(*this) -= b; }
Fixed_matrix operator*(const T& c) const { return Fixed_matrix(*this) *= c; }
friend Fixed_matrix operator*(const T& c, const Fixed_matrix& a) { return a * c; }
Fixed_matrix operator-() const { return Fixed_matrix(*this) *= T(-1); }
// : O(n^2)
array<T, n> operator*(const array<T, n>& x) const {
array<T, n> y{ 0 };
rep(i, n) rep(j, n) y[i] += v[i][j] * x[j];
return y;
}
// : O(n^2)
friend array<T, n> operator*(const array<T, n>& x, const Fixed_matrix& a) {
array<T, n> y{ 0 };
rep(i, n) rep(j, n) y[j] += x[i] * a[i][j];
return y;
}
// O(n^3)
Fixed_matrix operator*(const Fixed_matrix& b) const {
// verify : https://yukicoder.me/problems/no/1000
Fixed_matrix res;
rep(i, n) rep(j, n) rep(k, n) res[i][j] += v[i][k] * b[k][j];
return res;
}
Fixed_matrix& operator*=(const Fixed_matrix& b) { *this = *this * b; return *this; }
// O(n^3 log d)
Fixed_matrix pow(ll d) const {
Fixed_matrix res(true), pow2(*this);
while (d > 0) {
if (d & 1) res *= pow2;
pow2 *= pow2;
d /= 2;
}
return res;
}
#ifdef _MSC_VER
friend ostream& operator<<(ostream& os, const Fixed_matrix& a) {
rep(i, n) {
os << "[";
rep(j, n) os << a[i][j] << " ]"[j == n - 1];
if (i < n - 1) os << "\n";
}
return os;
}
#endif
};
int main() {
// input_from_file("input.txt");
// output_to_file("output.txt");
ll n, m, k;
cin >> n >> m >> k;
array<mint, 2> vec{ 1, 0 };
ll l = m, pl = -1;
while (n > 0) {
Fixed_matrix<mint, 2> mat;
mat[0][0] = m / l - 1; mat[0][1] = m / l * (l - 1);
mat[1][0] = mat[0][0] + 1; mat[1][1] = mat[0][1] - 1;
vec = mat * vec;
pl = l;
ll g = gcd(l, k);
l /= g;
n--;
if (pl == l) {
mat = mat.pow(n);
vec = mat * vec;
break;
}
}
cout << vec[0] << endl;
}
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