제출 #20087

#제출 시각아이디문제언어결과실행 시간메모리
20087gs14004괄호 (kriii4_R)C++14
100 / 100
228 ms48596 KiB
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>
#include <limits.h>
#include <stack>
#include <queue>
#include <map>
#include <set>
#include <algorithm>
#include <string>
#include <functional>
#include <vector>
#include <numeric>
#include <deque>
#include <utility>
#include <bitset>
#include <iostream>
using namespace std;
typedef long long lint;
typedef long double llf;
typedef pair<int, int> pi;
const int mod = 1e9 + 7;

lint fact[2000005];
lint cat[2000005];
lint dp[2000005];

lint ipow(lint x, lint p){
    lint ret = 1, piv = x % mod;
    while(p){
        if(p&1) ret *= piv;
        piv *= piv;
        ret %= mod;
        piv %= mod;
        p >>= 1;
    }
    return ret;
}
 
int main(){
	int n, k;
	cin >> n >> k;
	fact[0] = 1;
	for(int i=1; i<=n; i++){
		fact[i] = fact[i-1] * i % mod;
	}
	for(int i=0; i<=n/2; i++){
		cat[i] = fact[2*i] * ipow(fact[i+1] * fact[i], mod - 2) % mod;
	}
	dp[0] = 1;
	for(int i=1; i<=n; i++){
		if(i%2 == 0){
			dp[i] = dp[i-1] * (k+1) % mod;
		}
		else{
			dp[i] = dp[i-1] * (k+1) % mod - cat[i/2] * ipow(k, i/2) % mod + mod;
			dp[i] %= mod;
		}
	}
	cout << dp[n];
}
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