結果

問題 No.2896 Monotonic Prime Factors
ユーザー pitPpitP
提出日時 2024-09-21 00:11:06
言語 C++23(gcc13)
(gcc 13.2.0 + boost 1.83.0)
結果
AC  
実行時間 301 ms / 2,000 ms
コード長 6,295 bytes
コンパイル時間 7,096 ms
コンパイル使用メモリ 338,304 KB
実行使用メモリ 51,552 KB
最終ジャッジ日時 2024-09-21 00:11:22
合計ジャッジ時間 12,670 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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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 129 ms
51,456 KB
testcase_01 AC 102 ms
51,492 KB
testcase_02 AC 93 ms
51,380 KB
testcase_03 AC 99 ms
51,520 KB
testcase_04 AC 262 ms
51,400 KB
testcase_05 AC 286 ms
51,504 KB
testcase_06 AC 301 ms
51,508 KB
testcase_07 AC 258 ms
51,496 KB
testcase_08 AC 263 ms
51,384 KB
testcase_09 AC 284 ms
51,328 KB
testcase_10 AC 198 ms
51,456 KB
testcase_11 AC 117 ms
51,384 KB
testcase_12 AC 110 ms
51,328 KB
testcase_13 AC 196 ms
51,520 KB
testcase_14 AC 220 ms
51,328 KB
testcase_15 AC 106 ms
51,552 KB
testcase_16 AC 136 ms
51,348 KB
testcase_17 AC 110 ms
51,368 KB
testcase_18 AC 290 ms
51,384 KB
testcase_19 AC 116 ms
51,528 KB
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ソースコード

diff #

#include <bits/stdc++.h>
#include <atcoder/all>
using namespace std;
using namespace atcoder;
istream &operator>>(istream &is, modint &a) { long long v; is >> v; a = v; return is; }
ostream &operator<<(ostream &os, const modint &a) { return os << a.val(); }
istream &operator>>(istream &is, modint998244353 &a) { long long v; is >> v; a = v; return is; }
ostream &operator<<(ostream &os, const modint998244353 &a) { return os << a.val(); }
istream &operator>>(istream &is, modint1000000007 &a) { long long v; is >> v; a = v; return is; }
ostream &operator<<(ostream &os, const modint1000000007 &a) { return os << a.val(); } 

typedef long long ll;
typedef vector<vector<int>> Graph;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
#define FOR(i,l,r) for (int i = l;i < (int)(r); i++)
#define rep(i,n) for (int i = 0;i < (int)(n); i++)
#define all(x) x.begin(), x.end()
#define rall(x) x.rbegin(), x.rend()
#define my_sort(x) sort(x.begin(), x.end())
#define my_max(x) *max_element(all(x))
#define my_min(x) *min_element(all(x))
template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; }
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; }
const int INF = (1<<30) - 1;
const ll LINF = (1LL<<62) - 1;
const double PI = acos(-1);
vector<int> di = {1,0,-1,0};
vector<int> dj = {0,1,0,-1};

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

// https://qiita.com/drken/items/3beb679e54266f20ab63
struct Eratosthenes{
    int N;
    vector<bool> isprime;
    vector<int> minfactor, mobius;
    Eratosthenes(int N_max = 1e7){init(N_max);}
    //初期化
    void init(int N_max = 1e7){
        int N = N_max;
        isprime.assign(N+1,true);
        minfactor.assign(N+1,-1);
        mobius.assign(N+1,1);
        //Eratosthenes O(NloglogN)
        isprime[0] = false;
        isprime[1] = false;
        for(int p=2;p<=N;p++){
            if (!isprime[p])continue;
            minfactor[p] = p;
            mobius[p] = -1;
            //pの倍数の処理
            for(int q=2*p;q<=N;q+=p){
                isprime[q] = false;
                if (minfactor[q] == -1){
                    minfactor[q] = p;
                }
                if ((q/p) % p == 0) mobius[q] = 0;
                else mobius[q] *= -1;
            }
        }
    }
    //素数判定,O(1)
    bool judge_prime(int num){
        return isprime[num];
    }
    //素数列挙,O(N)
    vector<int> list_primes(int num = -1){
        if (num == -1) num = N;
        vector<int> primes;
        for(int p=0;p<=num;p++){
            if (isprime[p]) primes.push_back(p);
        }
        return primes;
    }
    //高速素因数分解,O(logN),{(素因数,個数)...}
    vector<pii> factorize(int x){
        vector<pii> ans;
        while(x > 1){
            int p = minfactor[x];
            int e = 0;
            while(minfactor[x] == p){
                x /= p;
                e++;
            }
            ans.push_back(make_pair(p,e));
        }
        return ans;
    }
    //高速約数列挙 O(240(N <= 1e6),1344(N <= 1e9))
    vector<int> divisors(int x){
        vector<int> ans; ans.push_back(1);
        vector<pii> facts = factorize(x);
        for(auto [p,e]:facts){
            int s = ans.size();
            for(int i=0;i<s;i++){
                int v = 1;
                for(int j=0;j<e;j++){
                    v *= p;
                    ans.push_back(ans[i] * v);
                }
            }
        }
        sort(all(ans));
        return ans;
    }
    //オイラーのphi関数
    ll euler_phi(int x){
        auto facts = factorize(x);
        ll res = x;
        for(auto [p, e]:facts){
            res = res - res / p;
        }
        return res;
    }
    //メビウス関数
    //mobius[1] = 1
    //nが素数pで2回以上割り切れる -> mobius[n] = 0
    //mobius[n] = pow(-1,Nの素数の種類)
    int my_mobius(int x){
        return mobius[x];
    }
};

// f -> F, 累積和Fを求める
template<typename T>
vector<T> fast_zeta(vector<T> &f){
    vector<T> res = f;
    int N = f.size() - 1; 
    Eratosthenes er(N);
    for(int p=2;p<=N;p++){
        if (!er.judge_prime(p)) continue;
        for(int k=(N/p);k>0;k--){
            res[k] += res[k * p];
        }
    }
    return res;
}

// F -> f, 累積和Fを分解する
template<typename T>
vector<T> fast_mobius(vector<T> &F){
    vector<T> res = F;
    int N = F.size() - 1; 
    Eratosthenes er(N);
    for(int p=2;p<=N;p++){
        if (!er.judge_prime(p)) continue;
        for(int k=1;k<=(N/p);k++){
            res[k] -= res[k * p];
        }
    }
    return res;
}

template<typename T>
vector<T> gcd_conv(vector<T> &f, vector<T> &g){
    int N = max(f.size(), g.size());
    vector<T> F(N+1) , G(N+1), H(N+1);
    for(int i=0;i<f.size();i++){
        F[i] = f[i];
    }
    for(int i=0;i<g.size();i++){
        G[i] = g[i];
    }
    F = fast_zeta(F);
    G = fast_zeta(G);
    for(int i=1;i<=N;i++){
        H[i] = F[i] * G[i];
    }
    H = fast_mobius(H);
    return H;
}

const int L = 100000;

//https://drken1215.hatenablog.com/entry/2018/06/08/210000
//COMinit()を忘れない!!!
const ll NMAX = 2020200;
const ll MOD = 998244353;
//const int MOD = 1e9+7;

ll fac[NMAX],finv[NMAX],inv[NMAX];

void COMinit(){
    fac[0] = fac[1] = 1LL;
    finv[0] = finv[1] = 1LL;
    inv[1] = 1LL;
    for (int i=2;i<NMAX;i++){
        fac[i] = fac[i-1] * i % MOD;
        inv[i] = MOD - inv[MOD%i] * (MOD/i) % MOD;
        finv[i] = finv[i-1] * inv[i] % MOD;
    }
}

ll nCr(int n,int k){
    if (n<k) return 0LL;
    if (n < 0 || k < 0) return 0LL;
    return fac[n] * (finv[k] * finv[n-k] % MOD) % MOD;
}

ll nPr(int n,int k){
    if (n<k) return 0LL;
    if (n < 0 || k < 0) return 0LL;
    return fac[n] * finv[n-k] % MOD;
}

ll nHr(int n,int r){
    return nCr(n+r-1,r);
}

int main(){
    cin.tie(0);
    ios_base::sync_with_stdio(false);

    COMinit();
    Eratosthenes er(L);

    int N = 0;
    int Q; cin >> Q;
    while(Q--){
        int A, B; cin >> A >> B;
        for(auto [p, e] : er.factorize(A)){
            N += e;
        }

        cout << nCr(N - 1, B - 1) << endl;
    }

}
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