CodeForces 838D Airplane Arrangements

洛谷传送门

CF 传送门

考虑加入第 \(n + 1\) 个位置，这样座位构成了一个环。每个位置被覆盖的概率相等，为 \(\frac{m}{n + 1}\)，然后算出概率再乘方案数就行了。

code

// Problem: D. Airplane Arrangements
// Contest: Codeforces - IndiaHacks 2nd Elimination 2017 (unofficial, unrated mirror, ICPC rules)
// URL: https://codeforces.com/problemset/problem/838/D
// Memory Limit: 256 MB
// Time Limit: 2000 ms
// 
// Powered by CP Editor (https://cpeditor.org)

#include <bits/stdc++.h>
#define pb emplace_back
#define fst first
#define scd second
#define mkp make_pair
#define mems(a, x) memset((a), (x), sizeof(a))

using namespace std;
typedef long long ll;
typedef double db;
typedef unsigned long long ull;
typedef long double ldb;
typedef pair<ll, ll> pii;

const ll mod = 1000000007;

inline ll qpow(ll b, ll p) {
	ll res = 1;
	while (p) {
		if (p & 1) {
			res = res * b % mod;
		}
		b = b * b % mod;
		p >>= 1;
	}
	return res;
}

ll n, m;

void solve() {
	scanf("%lld%lld", &n, &m);
	printf("%lld\n", (n + 1 - m) * qpow(n + 1, mod - 2) % mod * qpow(2 * (n + 1), m) % mod);
}

int main() {
	int T = 1;
	// scanf("%d", &T);
	while (T--) {
		solve();
	}
	return 0;
}