結果

問題 No.368 LCM of K-products
ユーザー tskrex
提出日時 2016-07-05 00:26:27
言語 C++11（廃止可能性あり）
(gcc 13.3.0)
結果
AC  
実行時間 73 ms / 2,000 ms
コード長 4,948 bytes
コンパイル時間 1,249 ms
コンパイル使用メモリ 113,000 KB
実行使用メモリ 17,536 KB
最終ジャッジ日時 2024-09-22 14:50:26
合計ジャッジ時間 2,798 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge2
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ファイルパターン 結果
other AC * 35
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 # 

#include <algorithm>
#include <cassert>
#include <climits>
#include <cmath>
#include <cstdio>
#include <cstdlib>
#include <deque>
#include <iomanip>
#include <iostream>
#include <limits>
#include <map>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <vector>

#define FOR(i,k,n) for (int (i)=(k); (i)<(n); ++(i))
#define rep(i,n) FOR(i,0,n)
#define pb push_back
#define eb emplace_back
#define all(v) begin(v), end(v)
#define debug(x) cerr<< #x <<": "<<x<<endl
#define debug2(x,y) cerr<< #x <<": "<< x <<", "<< #y <<": "<< y <<endl

using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef pair<int, int> i_i;
typedef pair<i_i, int> p_i;
typedef vector<int> vi;
typedef vector<vector<int> > vvi;
typedef vector<ll> vll;
typedef vector<vector<ll> > vvll;
typedef vector<char> vc;
typedef vector<vector<char> > vvc;
typedef vector<double> vd;
typedef vector<vector<double> > vvd;
template<class T> using vv=vector<vector< T > >;
typedef deque<int> di;
typedef deque<deque<int> > ddi;

// cout vector
template<typename T> ostream& operator<<(ostream& s, const vector<T>& v) {
    int len = v.size();
    for (int i = 0; i < len; ++i) {
        s << v[i]; if (i < len - 1) s << "\t";
    }
    return s;
}

// cout 2-dimentional vector
template<typename T> ostream& operator<<(ostream& s, const vector< vector<T> >& vv) {
    int len = vv.size();
    for (int i = 0; i < len; ++i) {
        s << vv[i] << endl;
    }
    return s;
}

int MAX_PRIME; // in this problem up to 10^4.5
deque<bool> isprime;
vector<int> primes;
void init_prime() {
    isprime[0] = isprime[1] = false;
    for(int i = 2; i <= MAX_PRIME; i++) {
        if (isprime[i]) {
            primes.push_back(i);
            for(int j = i*2; j <= MAX_PRIME; j += i)
                isprime[j] = false;
        }
    }
}

template<long long M>
struct ModInt {
    long long x;
    ModInt() : x(0) {}
    ModInt(long long y) : x(y >= 0 ? y % M : M - (-y) % M) {}
    ModInt &operator += (const ModInt &rhs){ if((x += rhs.x) >= M) x -= M; return *this; }
    ModInt &operator -= (const ModInt &rhs){ if((x += M - rhs.x) >= M) x -= M; return *this; }
    ModInt &operator *= (const ModInt &rhs){ x = 1LL*x*rhs.x % M; return *this; }
    ModInt &operator /= (const ModInt &rhs){ x = (1LL*x*rhs.inv().x) % M; return *this; }
    ModInt operator - () const { return ModInt(-x); }
    ModInt operator + (const ModInt &rhs) const { return ModInt(*this) += rhs; }
    ModInt operator - (const ModInt &rhs) const { return ModInt(*this) -= rhs; }
    ModInt operator * (const ModInt &rhs) const { return ModInt(*this) *= rhs; }
    ModInt operator / (const ModInt &rhs) const { return ModInt(*this) /= rhs; }
    bool operator < (const ModInt &rhs) const { return x < rhs.x; }
    ModInt inv() const {
        long long a = x, b = M, u = 1, v = 0, t;
        while(b){ t = a / b; a -= t * b; swap(a, b); u -= t * v; swap(u, v); }
        return ModInt(u);
    }
    ModInt pow(long long t) const {
        ModInt e = *this, res = 1;
        for(; t; e *= e, t>>=1) if(t&1) res *= e;
        return res;
    }
};
template <long long M>
ostream &operator << (ostream &os, const ModInt<M> &rhs){
    return os << rhs.x;
}
template <long long M>
istream &operator >> (istream &is, ModInt<M> &rhs){
    long long s; is >> s; rhs = ModInt<M>(s); return is;
};

int pow_mod(ll x, ll n, ll m) {
    ll res = 1;
    for (; n > 0; n >>= 1) {
        if (n & 1) res = (res * x) % m;
        x = (x * x) % m;
    }
    return res;
}

int main() {
    MAX_PRIME = sqrt(1000000000);
    isprime.resize(MAX_PRIME+1, true);
    init_prime();
    int n, k;
    cin >> n >> k;
    vi a(n);
    vvi factors(primes.size());
    map<int, int> big_primes;
    rep (i, n) { cin >> a[i]; }
    rep (i, n) {
        rep (j, primes.size()) {
//            if ( primes[j] * primes[j] > a[i] ) {
//                break;
//            }
            int cnt = 0;
            while ( a[i] % primes[j] == 0 ) {
                a[i] /= primes[j];
                cnt += 1;
            }
            factors[j].pb(cnt);
            if ( a[i] == 1 ) {
                break;
            }
        }
        if ( a[i] > 1 ) {
            big_primes[a[i]] += 1;
            debug(i);
        }
    }
    rep (i, factors.size()) {
        sort(all(factors[i]), [](int x, int y) {
            return x > y;
        });
        if ( factors[i].size() > k ) {
            factors[i].erase(begin(factors[i])+k, end(factors[i]));
        }
    }

    const ll mod = 1000000007;
    ModInt<mod> ans(1);
    // small primes
    rep (i, factors.size()) {
        int cnt = 0;
        rep (j, factors[i].size()) {
            cnt += factors[i][j];
        }
        ans *= pow_mod(primes[i], cnt, mod);
    }
    // big primes
    for (auto bp : big_primes) {
        ans *= pow_mod(bp.first, min(k, bp.second), mod);
    }
    printf("%lld\n", ans.x);

    return 0;
}
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