Submission #19324

#	Time	Username	Problem	Language	Result	Execution time	Memory
19324		cki86201	Ω (kriii4_P3)	C++14	100 / 100	0 ms	1816 KiB

P3

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <memory.h>
#include <math.h>
#include <assert.h>
#include <stack>
#include <queue>
#include <map>
#include <set>
#include <string>
#include <algorithm>
#include <iostream>
#include <functional>

using namespace std;
typedef long long ll;
typedef pair<int, int> Pi;
#define Fi first
#define Se second
#define pb(x) push_back(x)
#define sz(x) (int)x.size()
#define rep(i,n) for(int i=0;i<n;i++)
#define all(x) x.begin(),x.end()

const ll MOD = 1e9 + 7;

ll pw(ll a,ll b){
	a %= MOD;
	ll res = 1;
	while(b){
		if(b&1)res = (res * a) % MOD;
		a = (a * a) % MOD;
		b >>= 1;
	}
	return res;
}

ll b[110];
ll M[110][110];

int main(){
	int p, q, n, k;
	scanf("%d%d%d%d", &p, &q, &n, &k);
	if(k == 0)printf("0");
	else if(k == n)printf("1");
	else{
	ll p1 = (q * pw(p, MOD-2)) % MOD;
	ll p2 = (MOD + 1 - p1) % MOD;
	for(int i=1;i<n;i++){
		M[i][i] = 1;
		if(i != n)M[i][i+1] = (MOD - p2) % MOD;
		if(i != 1)M[i][i-1] = (MOD - p1) % MOD;
	}
	b[n-1] = p2;
	--n;
	for(int i=1;i<=n;i++){
		ll tmp = pw(M[i][i], MOD-2) % MOD;
		for(int j=i;j<=n;j++){
			M[i][j] = (M[i][j] * tmp) % MOD;
		}
		b[i] = (b[i] * tmp) % MOD;
		for(int j=i+1;j<=n;j++){
			if(M[i][j] == 0)continue;
			ll mul = M[j][i];
			for(int k=i;k<=n;k++)M[j][k] = ((M[j][k] - mul * M[i][k]) % MOD + MOD) % MOD;
			b[j] = ((b[j] - mul * b[i]) % MOD + MOD) % MOD;
		}
	}
	//for(int i=1;i<=n;i++){for(int j=1;j<=n;j++)printf("%lld ", M[i][j]);puts("");}
	for(int i=n;i>=1;i--){
		for(int j=i-1;j>=1;j--){
			b[j] -= b[i] * M[j][i] % MOD;
			b[j] = (b[j] + MOD) % MOD;
		}
	}
	printf("%lld", b[k]);
	}
	return 0;
}

• Subtask 1: 100 / 100