Submission #19446

#	Time	Username	Problem	Language	Result	Execution time	Memory
19446		xhae	Ω (kriii4_P3)	C++14	100 / 100	0 ms	1724 KiB

P3

#include <iostream>
#include <cmath>
#include <algorithm>

using namespace std;

const long long MOD = 1000000007;
long long P, Q, N, K;
long long p[101], q[101], d[101];

long long inv(long long tar) {
	long long ret = 1;
	for(int i = 30; i >= 0; i--) {
		ret = ret * ret % MOD;
		if((1ll << i) & (MOD - 2)) ret = ret * tar % MOD;
	}
	return ret;
}

int main(void) {
	cin >> P >> Q >> N >> K;
	if(K == 0) printf("0\n");
	else if(K == N) printf("1\n");
	else {
		long long gcdv = __gcd(Q, P);
		long long a = Q / gcdv * inv(P / gcdv) % MOD;
		gcdv = __gcd(P - Q, P);
		long long b = (P - Q) / gcdv * inv(P / gcdv) % MOD;

		p[N - 1] = a, q[N - 1] = b;
		for(int i = N - 2; i > 0; i--) {
			long long base = ((1 - b * p[i + 1] % MOD) + MOD) % MOD;
			p[i] = a * inv(base) % MOD;
			q[i] = b * q[i + 1] % MOD * inv(base) % MOD;
		}
		d[0] = 0;
		for(int i = 1; i < N; i++) d[i] = (d[i - 1] * p[i] % MOD + q[i]) % MOD;
		cout << d[K];
	}


	return 0;
}

• Subtask 1: 100 / 100