結果

問題 No.2896 Monotonic Prime Factors
ユーザー ecotteaecottea
提出日時 2024-09-20 21:48:05
言語 C++17(gcc12)
(gcc 12.3.0 + boost 1.87.0)
結果
AC  
実行時間 149 ms / 2,000 ms
コード長 12,453 bytes
コンパイル時間 7,082 ms
コンパイル使用メモリ 313,300 KB
実行使用メモリ 42,876 KB
最終ジャッジ日時 2024-09-20 21:48:17
合計ジャッジ時間 10,283 ms
ジャッジサーバーID
(参考情報)
judge1 / 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 * 2
other AC * 18
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

// QCFium
#pragma GCC target("avx2")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#ifndef HIDDEN_IN_VS //
//
#define _CRT_SECURE_NO_WARNINGS
//
#include <bits/stdc++.h>
using namespace std;
//
using ll = long long; using ull = unsigned long long; // -2^63 2^63 = 9e18int -2^31 2^31 = 2e9
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);
int DX[4] = { 1, 0, -1, 0 }; // 4
int DY[4] = { 0, 1, 0, -1 };
int INF = 1001001001; ll INFL = 4004004003094073385LL; // (int)INFL = INF, (int)(-INFL) = -INF;
//
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##_ub = 1 << int(d); set < set##_ub; ++set) // d
#define repis(i, set) for(int i = lsb(set), bset##i = set; i < 32; bset##i -= 1 << i, i = lsb(bset##i)) // set
#define repp(a) sort(all(a)); for(bool a##_perm = true; a##_perm; a##_perm = next_permutation(all(a))) // a
#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 powi(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 getb(T set, int i) { return (set >> i) & T(1); }
template <class T> inline T smod(T n, T m) { n %= m; if (n < 0) n += m; return n; } // mod
//
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 = static_modint<1234567891>;
//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>; using pim = pair<int, mint>;
#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) : 32; }
inline int lsb(ll n) { return n != 0 ? __builtin_ctzll(n) : 64; }
template <size_t N> inline int lsb(const bitset<N>& b) { return b._Find_first(); }
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; }
#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)) { vc MLE(1<<30); EXIT(MLE.back()); } } // RE MLE
#endif
//
/*
* Osa_k(int n) : O(n log(log n))
* n
*
* bool primeQ(int i) : O(1)
* i
*
* map<int, int> factor_integer(int i) : O(log n)
* i
*
* vi divisors(int i) : O(σ(n))
* i
*
* int euler_phi(int i) : O(log n)
* φ(i)
*
* int radical(int i) : O(log n)
* i
*
* vi prime_power_decomposition(int i) : O(log n)
* i
*/
struct Osa_k {
int n;
// gpf[i] : i
vi gpf;
// n
Osa_k(int n_) : n(n_), gpf(n + 1) {
// verify : https://yukicoder.me/problems/no/2207
iota(all(gpf), 0);
for (int p = 2; p * p <= n; p++) {
if (gpf[p] != p) continue;
// d p^2
for (int i = p; i <= n; i += p) gpf[i] = p;
}
}
Osa_k() : n(0) {}
// i
bool primeQ(int i) {
// verify : https://yukicoder.me/problems/no/1396
Assert(i <= n);
return i >= 2 && gpf[i] == i;
}
// i
map<int, int> factor_integer(int i) const {
// verify : https://yukicoder.me/problems/no/2207
Assert(i <= n);
map<int, int> pps;
while (i > 1) {
pps[gpf[i]]++;
i /= gpf[i];
}
return pps;
}
// i
vi divisors(int i) const {
// verify : https://atcoder.jp/contests/abc368/tasks/abc368_f
Assert(i <= n);
vi divs{ 1 };
auto pps = factor_integer(i);
for (auto [p, d] : pps) {
vi powp(d);
powp[0] = p;
rep(i, d - 1) powp[i + 1] = powp[i] * p;
int m = sz(divs);
repir(j, m - 1, 0) rep(i, d) divs.push_back(divs[j] * powp[i]);
}
sort(all(divs)); //
return divs;
}
// φ(i)
int euler_phi(int i) {
// verify : https://yukicoder.me/problems/no/2849
Assert(i <= n);
int phi = 1; int pp = INF;
while (i > 1) {
int p = gpf[i];
phi *= (p == pp ? p : p - 1);
pp = p;
i /= p;
}
return phi;
}
// i
int radical(int i) const {
// verify : https://projecteuler.net/problem=518
Assert(i <= n);
int rad = 1; int pp = INF;
while (i > 1) {
int p = gpf[i];
if (p != pp) rad *= p;
pp = p;
i /= p;
}
return rad;
}
// i
vi prime_power_decomposition(int i) const {
// verify : https://projecteuler.net/problem=407
Assert(i <= n);
vi res; int pp = INF;
while (i > 1) {
int p = gpf[i];
if (p != pp) res.push_back(p);
else res.back() *= p;
pp = p;
i /= p;
}
return res;
}
};
//
/*
* Factorial_mint(int N) : O(n)
* N
*
* mint fact(int n) : O(1)
* n!
*
* mint fact_inv(int n) : O(1)
* 1/n! n 0
*
* mint inv(int n) : O(1)
* 1/n
*
* mint perm(int n, int r) : O(1)
* nPr
*
* mint bin(int n, int r) : O(1)
* nCr
*
* mint bin_inv(int n, int r) : O(1)
* 1/nCr
*
* mint mul(vi rs) : O(|rs|)
* nC[rs] n = Σrs
*
* mint hom(int n, int r) : O(1)
* nHr = n+r-1Cr 0H0 = 1
*
* mint neg_bin(int n, int r) : O(1)
* nCr = (-1)^r -n+r-1Cr n ≦ 0, r ≧ 0
*/
class Factorial_mint {
int n_max;
//
vm fac, fac_inv;
public:
// n! O(n)
Factorial_mint(int n) : n_max(n), fac(n + 1), fac_inv(n + 1) {
// verify : https://atcoder.jp/contests/dwacon6th-prelims/tasks/dwacon6th_prelims_b
fac[0] = 1;
repi(i, 1, n) fac[i] = fac[i - 1] * i;
fac_inv[n] = fac[n].inv();
repir(i, n - 1, 0) fac_inv[i] = fac_inv[i + 1] * (i + 1);
}
Factorial_mint() : n_max(0) {} //
// n!
mint fact(int n) const {
// verify : https://atcoder.jp/contests/dwacon6th-prelims/tasks/dwacon6th_prelims_b
Assert(0 <= n && n <= n_max);
return fac[n];
}
// 1/n! n 0
mint fact_inv(int n) const {
// verify : https://atcoder.jp/contests/abc289/tasks/abc289_h
Assert(n <= n_max);
if (n < 0) return 0;
return fac_inv[n];
}
// 1/n
mint inv(int n) const {
// verify : https://atcoder.jp/contests/exawizards2019/tasks/exawizards2019_d
Assert(0 < n && n <= n_max);
return fac[n - 1] * fac_inv[n];
}
// nPr
mint perm(int n, int r) const {
// verify : https://atcoder.jp/contests/abc172/tasks/abc172_e
Assert(n <= n_max);
if (r < 0 || n - r < 0) return 0;
return fac[n] * fac_inv[n - r];
}
// nCr
mint bin(int n, int r) const {
// verify : https://judge.yosupo.jp/problem/binomial_coefficient_prime_mod
Assert(n <= n_max);
if (r < 0 || n - r < 0) return 0;
return fac[n] * fac_inv[r] * fac_inv[n - r];
}
// 1/nCr
mint bin_inv(int n, int r) const {
// verify : https://www.codechef.com/problems/RANDCOLORING
Assert(n <= n_max);
Assert(r >= 0 || n - r >= 0);
return fac_inv[n] * fac[r] * fac[n - r];
}
// nC[rs]
mint mul(const vi& rs) const {
// verify : https://yukicoder.me/problems/no/2141
if (*min_element(all(rs)) < 0) return 0;
int n = accumulate(all(rs), 0);
Assert(n <= n_max);
mint res = fac[n];
repe(r, rs) res *= fac_inv[r];
return res;
}
// nHr = n+r-1Cr 0H0 = 1
mint hom(int n, int r) {
// verify : https://mojacoder.app/users/riantkb/problems/toj_ex_2
if (n == 0) return (int)(r == 0);
Assert(n + r - 1 <= n_max);
if (r < 0 || n - 1 < 0) return 0;
return fac[n + r - 1] * fac_inv[r] * fac_inv[n - 1];
}
// nCr n ≦ 0, r ≧ 0
mint neg_bin(int n, int r) {
// verify : https://atcoder.jp/contests/abc345/tasks/abc345_g
if (n == 0) return (int)(r == 0);
Assert(-n + r - 1 <= n_max);
if (r < 0 || -n - 1 < 0) return 0;
return (r & 1 ? -1 : 1) * fac[-n + r - 1] * fac_inv[r] * fac_inv[-n - 1];
}
};
Factorial_mint fm((int)5e6 + 10);
int main() {
// input_from_file("input.txt");
// output_to_file("output.txt");
int m = (int)1e5;
Osa_k O(m);
int c = 0;
int q;
cin >> q;
rep(hoge, q) {
int a, b;
cin >> a >> b;
auto pps = O.factor_integer(a);
for (auto [p, e] : pps) c += e;
cout << fm.bin(c - 1, b - 1) << "\n";
}
}
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