結果

問題 No.2326 Factorial to the Power of Factorial to the...
ユーザー EtisEtis
提出日時 2023-05-28 14:42:23
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
WA  
実行時間 -
コード長 7,700 bytes
コンパイル時間 4,312 ms
コンパイル使用メモリ 270,848 KB
実行使用メモリ 79,744 KB
最終ジャッジ日時 2024-06-08 06:03:07
合計ジャッジ時間 6,063 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge3
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 8 ms
9,536 KB
testcase_01 WA -
testcase_02 AC 26 ms
23,520 KB
testcase_03 AC 95 ms
62,080 KB
testcase_04 WA -
testcase_05 AC 45 ms
35,456 KB
testcase_06 AC 88 ms
55,296 KB
testcase_07 WA -
testcase_08 WA -
testcase_09 WA -
testcase_10 AC 8 ms
10,688 KB
testcase_11 AC 16 ms
18,816 KB
testcase_12 AC 5 ms
8,448 KB
testcase_13 WA -
testcase_14 AC 105 ms
68,196 KB
testcase_15 WA -
testcase_16 AC 4 ms
5,376 KB
testcase_17 WA -
testcase_18 WA -
testcase_19 AC 11 ms
12,288 KB
testcase_20 AC 2 ms
5,376 KB
testcase_21 AC 1 ms
5,376 KB
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ソースコード

diff # 

//#pragma GCC target("avx")
//#pragma GCC optimize("Ofast")
//#pragma GCC optimize("unroll-loops")
//#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")

#include <bits/stdc++.h>
using namespace std;
#include <atcoder/all>
using namespace atcoder;

//local debug
#ifdef LOCAL
#include <debug_print.hpp>
#define debug(...) debug_print::multi_print(#__VA_ARGS__, __VA_ARGS__)
#else
#define debug(...) (static_cast<void>(0))
#endif

#define overload4(a, b, c, d, e, ...) e

//alias
using uint = unsigned int;
using ll = long long;
using ull = unsigned long long;
using ld = long double;
using mint = modint998244353;
using Mint = modint1000000007;

//constants
constexpr const long long MOD = 998244353;
constexpr const long long MODM = 1000000007;
constexpr const int INF = 1e9;
constexpr const ll LINF = 1e18;

//rep(for-loop) macro
#define rep2(i, n) for(ll i = 0; i < n; i++)
#define rep3(i, k, n) for(ll i = k; i < n; i++)
#define rep4(i, k, n, a) for(ll i = k; i < n; i += a)
#define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2)(__VA_ARGS__)
#define rep1_2(i, n) for(ll i = 1; i <= n; i++)
#define rep1_3(i, k, n) for(ll i = k; i <= n; i++)
#define rep1_4(i, k, n, a) for(ll i = k; i <= n; i += a)
#define rep1(...) overload4(__VA_ARGS__, rep1_4, rep1_3, rep1_2)(__VA_ARGS__)
#define Rep2(i, n) for(ll i = n - 1; i >= 0; i--)
#define Rep3(i, k, n) for(ll i = n - 1; i >= k; i--)
#define Rep4(i, k, n, a) for(ll i = n - 1; i >= k; i -= a) 
#define Rep(...) overload4(__VA_ARGS__, Rep4, Rep3, Rep2)(__VA_ARGS__)
#define Rep1_2(i, n) for(ll i = n; i >= 1; i--)
#define Rep1_3(i, k, n) for(ll i = n; i >= k; i--)
#define Rep1_4(i, k, n, a) for(ll i = n; i >= k; i -= a) 
#define Rep1(...) overload4(__VA_ARGS__, Rep1_4, Rep1_3, Rep1_2)(__VA_ARGS__)
#define vfor(v, x) for(auto x : v)
#define mfor(map) for(auto &[key, value] : map)

//vector macro
#define vvecc(T, name, n, m) vector<vector<T>> name(n, vector<T>(m))
#define vvec(T, name, n) vector<vector<T>> name(n)
#define vvecs(T, name, n, m, s) vector<vector<T>> name(n, vector<T>(m, s))
#define all(x) begin(x), end(x)
#define LB(v, x) distance((v).begin(), lower_bound(all(v), (x)))
#define UB(v, x) distance((v).begin(), upper_bound(all(v), (x)))

//data structure macro
#define ef emplace_front
#define eb emplace_back
#define pf pop_front
#define pb pop_back
#define mp make_pair
#define fi first
#define se second
#define mt make_tuple
#define get(t, x) get<x - 1>(t)
#define lb lower_bound
#define ub upper_bound
template<class T> using pq = priority_queue<T>;
template<class T> using pqmin = priority_queue<T, vector<T>, greater<T>>;
template<class T, class U> using pqp = priority_queue<pair<T, U>>;
template<class T, class U> using pqpmin = priority_queue<pair<T, U>, vector<pair<T, U>>, greater<pair<T,U>>>;

//output
#define pl() cout << '\n'
template<class T> void print(const T& a) {cout << a;}
void printl(){}
template<class T> void printl(const T& t){print(t); pl();}
template<class Head, class... Tail> void printl(const Head& head, const Tail&... tail) {print(head); cout << " "; printl(tail...);}
template<class T> void fin(const T& t) {printl(t); exit(0);}
void Yes(bool a) {cout << (a ? "Yes" : "No") << '\n';}
template<class T, class U> void Out2(bool a, T yes, U no) {if(a) printl(yes); else printl(no);}

//functions
int ctoi(char c) {return c - '0';}
char to_char(int x) {return x + '0';}
template<class... T> constexpr auto Emin(T... a) {return min(initializer_list<common_type_t<T...>>{a...});}
template<class... T> constexpr auto Emax(T... a) {return max(initializer_list<common_type_t<T...>>{a...});}
template<class T, class U> bool chmax(T &a, const U &b) {if (a < b) { a = b; return true;} return false;}
template<class T, class U> bool chmin(T &a, const U &b) {if (a > b) { a = b; return true;} return false;}
template<class T, class U> ll Epow(T x, U y) {ll ans = 1; for(int i = 0; i < y; i++) ans *= x; return ans;}
template<class T, class U> ll Eceil(T x, U y) {return (ll)ceil((ld)x / (ld)y);}
template<class T, class U> ll Efloor(T x, U y) {return (ll)floor((ld)x / (ld)y);}
template<class T, class U> bool check_bit(T tar, U bit) {return ((tar & Epow(2, bit)) != 0);}

/*Math Library<ACL>*/
//a ÷ bをmodで割った余り(modは素数) - O(log(mod))
ll div_mod(ll a, ll b, ll mod) {return (a * pow_mod(b, mod - 2, mod)) % mod;}

//階乗 - O(n)
ll factorial(ll n, ll mod) {
    ll ans = 1;
    for(ll i = n; i >= 2; i--) ans = (ans * i) % mod;
    return ans;
}ll factorial(ll n) {return factorial(n, MOD);}

//順列 - O(r)
ll permutation(ll n, ll r, ll mod) {
    ll ans = 1;
    for(ll i = 0; i < r; i++) ans = (ans * (n - i)) % mod;
    return ans;
}ll permutation(ll n, ll r) {return permutation(n, r, MOD);}

//組み合わせ(modは素数) - O(min(r, n - r) + log(mod))
ll combination(ll n, ll r, ll mod) {
    r = min(r, n - r);
    if(r == 0) return 1;
    ll up = n;
    ll down = 1;
    for(int i = 1; i < r; i++) {
        up = (up * (n - i)) % mod;
        down = (down * (i + 1)) % mod;
    }
    return div_mod(up, down, mod);
}ll combination(ll n, ll r) {return combination(n, r, MOD);}

//nC0~nCrまでの列挙(modは素数) - O(rlog(mod))
vector<ll> getCombination_vec(ll n, ll r, ll mod) {
    vector<ll> ret(r + 1);
    ret[0] = 1;
    ll up = n;
    ll down = 1;
    ret[1] = div_mod(up, down, mod);
    for(int i = 1; i < r; i++) {
        up = (up * (n - i)) % mod;
        down = (down * (i + 1)) % mod;
        ret[i + 1] = div_mod(up, down, mod);
    }
    return ret;
}vector<ll> getCombination_vec(ll n, ll r) {return getCombination_vec(n, r, MOD);}

//素数判定 - O(√N)
bool is_prime(ll N) {
    if (N == 1) return false;
    for (ll i = 2; i * i <= N; i++) {
        if (N % i == 0) return false;
    }
    return true;
}

//約数列挙 - O(√N)
vector<ll> enum_divisors(ll N) {
    vector<ll> res;
    for (ll i = 1; i * i <= N; i++) {
        if (N % i == 0) {
            res.eb(i);
            if (N / i != i) res.eb(N / i);
        }
    }
    sort(all(res));
    return res;
}

//素因数分解 - O(√N)
vector<pair<ll, ll>> prime_factorize(ll N) {
    vector<pair<ll, ll>> res;
    for (ll a = 2; a * a <= N; a++) {
        if (N % a != 0) continue;
        ll ex = 0;
        while (N % a == 0) {
            ex++;
            N /= a;
        }
        res.eb(mp(a, ex));
    }
    if (N != 1) res.eb(mp(N, 1));
    return res;
}

//エラトステネスの篩 - O(NloglogN)
vector<bool> Eratosthenes(ll N) {
    vector<bool> isprime(N + 1, true);
    isprime[0] = isprime[1] = false;
    for (ll p = 2; p <= N; p++) {
        if (!isprime[p]) continue;
        for (ll q = p * 2; q <= N; q += p) {
            isprime[q] = false;
        }
    }
    return isprime;
}

//N以下の素数を列挙 - O(NloglogN)
vector<ll> getPrimes(ll N) {
    vector<bool> era = Eratosthenes(N);
    vector<ll> primes;
    for(ll i = 2; i <= N; i++) {
        if(era[i]) primes.eb(i);
    }
    return primes;
}

//---------------------------------------------------------------------------------------------------
int main() {

    ios::sync_with_stdio(false);
    cin.tie(0);
    cout << fixed << setprecision(10);

    ll N, P;
    cin >> N >> P;

    vector<ll> prime_cnt((N + 1) * 100, 0);
    rep1(i, 2, N) {
        auto ret = prime_factorize(i);
        rep(j, ret.size()) prime_cnt[ret[j].fi] += ret[j].se;
    }

    auto need = prime_factorize(P);

    ll div_cnt = LINF;
    rep(i, need.size()) {
        ll cur = prime_cnt[need[i].fi] / need[i].se;
        div_cnt = Emin(div_cnt, cur);
    }

    ll Nfac = factorial(N, MODM);
    ll r = pow_mod(Nfac, Nfac, MODM);

    Mint ans = div_cnt;
    ans *= r;
    printl(ans.val());
}
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