結果

問題 No.377 背景パターン
コンテスト
ユーザー anta
提出日時 2016-06-05 01:06:27
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 418 ms / 5,000 ms
コード長 3,783 bytes
コンパイル時間 2,498 ms
コンパイル使用メモリ 183,008 KB
実行使用メモリ 5,248 KB
最終ジャッジ日時 2024-10-11 00:58:41
合計ジャッジ時間 3,632 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge4
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 * 5
other AC * 14
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 "bits/stdc++.h"
using namespace std;
#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))
static const int INF = 0x3f3f3f3f; static const long long INFL = 0x3f3f3f3f3f3f3f3fLL;
typedef vector<int> vi; typedef pair<int, int> pii; typedef vector<pair<int, int> > vpii; typedef long long ll;
template<typename T, typename U> static void amin(T &x, U y) { if(y < x) x = y; }
template<typename T, typename U> static void amax(T &x, U y) { if(x < y) x = y; }

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) { return *this *= that.inverse(); }

	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; }
	ModInt operator/(ModInt that) const { return ModInt(*this) /= that; }

	ModInt inverse() const {
		signed a = x, b = MOD, u = 1, v = 0;
		while(b) {
			signed t = a / b;
			a -= t * b; std::swap(a, b);
			u -= t * v; std::swap(u, v);
		}
		if(u < 0) u += Mod;
		ModInt res; res.x = (unsigned)u;
		return res;
	}
};
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;

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<typename T>T gcd(T x, T y) { if(y == 0)return x; else return gcd(y, x%y); }

void getDivisors(int N, vector<pair<int,int>> &res) {
	Factors fs;
	primeFactors(N, fs);
	res.emplace_back(1, 1);
	for(auto f : fs) {
		int p = f.first, k = f.second;
		for(int i = (int)res.size() - 1; i >= 0; -- i) {
			int d = res[i].first, t = res[i].second;
			t *= p - 1;
			for(int j = 1; j <= k; ++ j) {
				d *= p;
				res.emplace_back(d, t);
				t *= p;
			}
		}
	}
	sort(res.begin(), res.end());
}

int main() {
	sieve(100000);
	int H; int W; int K;
	while(~scanf("%d%d%d", &H, &W, &K)) {
		vector<pair<int,int>> divsH, divsW;
		getDivisors(H, divsH);
		getDivisors(W, divsW);
		mint ans;
		for(auto d : divsH) for(auto e : divsW) {
			int a = d.first, b = e.first;
			mint cnt = mint(K) ^ ((ll)W * H / a / b * gcd(a, b));
			ans += cnt * d.second * e.second;
		}
		ans /= (ll)H * W;
		printf("%d\n", ans.get());
	}
	return 0;
}
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