結果

問題 No.368 LCM of K-products
ユーザー anta
提出日時 2016-04-29 22:38:03
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 16 ms / 2,000 ms
コード長 3,621 bytes
コンパイル時間 1,368 ms
コンパイル使用メモリ 114,952 KB
実行使用メモリ 6,944 KB
最終ジャッジ日時 2024-09-22 14:41:06
合計ジャッジ時間 2,445 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge1
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ファイルパターン 結果
other AC * 35
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ソースコード

diff #
プレゼンテーションモードにする

#include <string>
#include <vector>
#include <algorithm>
#include <numeric>
#include <set>
#include <map>
#include <queue>
#include <iostream>
#include <sstream>
#include <cstdio>
#include <cmath>
#include <ctime>
#include <cstring>
#include <cctype>
#include <cassert>
#include <limits>
#include <functional>
#define rep(i,n) for(int (i)=0;(i)<(int)(n);++(i))
#define rer(i,l,u) for(int (i)=(int)(l);(i)<=(int)(u);++(i))
#define reu(i,l,u) for(int (i)=(int)(l);(i)<(int)(u);++(i))
#if defined(_MSC_VER) || __cplusplus > 199711L
#define aut(r,v) auto r = (v)
#else
#define aut(r,v) __typeof(v) r = (v)
#endif
#define each(it,o) for(aut(it, (o).begin()); it != (o).end(); ++ it)
#define all(o) (o).begin(), (o).end()
#define pb(x) push_back(x)
#define mp(x,y) make_pair((x),(y))
#define mset(m,v) memset(m,v,sizeof(m))
#define INF 0x3f3f3f3f
#define INFL 0x3f3f3f3f3f3f3f3fLL
using namespace std;
typedef vector<int> vi; typedef pair<int, int> pii; typedef vector<pair<int, int> > vpii; typedef long long ll;
template<typename T, typename U> inline void amin(T &x, U y) { if(y < x) x = y; }
template<typename T, typename U> inline void amax(T &x, U y) { if(x < y) x = y; }
vector<bool> isprime;
vector<int> primes;
void sieve(int n) {
    if((int)isprime.size() >= n + 1) return;
    isprime.assign(n + 1, true);
    isprime[0] = isprime[1] = false;
    int sqrtn = (int)(sqrt(n * 1.) + .5);
    for(int i = 2; i <= sqrtn; i ++) if(isprime[i]) {
        for(int j = i * i; j <= n; j += i)
            isprime[j] = false;
    }
    primes.clear();
    for(int i = 2; i <= n; i ++) if(isprime[i])
        primes.push_back(i);
}
typedef int FactorsInt;
typedef vector<pair<FactorsInt, int> > Factors;
void primeFactors(FactorsInt x, Factors &out_v) {
    out_v.clear();
    int sqrtx = (int)(sqrt(x*1.) + 10.5);
    sieve(sqrtx);
    for(vector<int>::const_iterator p = primes.begin(); p != primes.end(); ++ p) {
        if(*p > sqrtx) break;
        if(x % *p == 0) {
            int t = 1;
            x /= *p;
            while(x % *p == 0) {
                t ++;
                x /= *p;
            }
            out_v.push_back(make_pair(*p, t));
        }
    }
    if(x != 1) out_v.push_back(make_pair(x, 1));
}
template<int MOD>
struct ModInt {
    static const int Mod = MOD;
    unsigned x;
    ModInt() : x(0) {}
    ModInt(signed sig) { int sigt = sig % MOD; if(sigt < 0) sigt += MOD; x = sigt; }
    ModInt(signed long long sig) { int sigt = sig % MOD; if(sigt < 0) sigt += MOD; x = sigt; }
    int get() const { return (int)x; }
    ModInt &operator+=(ModInt that) { if((x += that.x) >= MOD) x -= MOD; return *this; }
    ModInt &operator-=(ModInt that) { if((x += MOD - that.x) >= MOD) x -= MOD; return *this; }
    ModInt &operator*=(ModInt that) { x = (unsigned long long)x * that.x % MOD; return *this; }
    ModInt operator+(ModInt that) const { return ModInt(*this) += that; }
    ModInt operator-(ModInt that) const { return ModInt(*this) -= that; }
    ModInt operator*(ModInt that) const { return ModInt(*this) *= that; }
};
template<int MOD> ModInt<MOD> operator^(ModInt<MOD> a, unsigned long long k) {
    ModInt<MOD> r = 1;
    while(k) {
        if(k & 1) r *= a;
        a *= a;
        k >>= 1;
    }
    return r;
}
typedef ModInt<1000000007> mint;
int main() {
    sieve(100000);
    int N; int K;
    while(~scanf("%d%d", &N, &K)) {
        vector<int> a(N);
        for(int i = 0; i < N; ++ i)
            scanf("%d", &a[i]);
        map<int, vi> primes;
        rep(i, N) {
            Factors fs;
            primeFactors(a[i], fs);
            for(auto t : fs)
                primes[t.first].push_back(t.second);
        }
        mint ans = 1;
        for(auto &t : primes) {
            vi &v = t.second;
            sort(all(v));
            reverse(all(v));
            int k = min((int)v.size(), K);
            int sum = 0;
            rep(i, k)
                sum += v[i];
            ans *= mint(t.first) ^ sum;
        }
        printf("%d\n", ans.get());
    }
    return 0;
}
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