There is a building with n rooms, numbered 1 to n.

We can move from any room to any other room in the building.

Let us call the following event a move: a person in some room i goes to another room j~ (i \neq j).

Initially, there was one person in each room in the building.

After that, we know that there were exactly k moves happened up to now.

We are interested in the number of people in each of the n rooms now. How many combinations of numbers of people in the n rooms are possible?

Find the count modulo (10^9 + 7).

Constraints

* All values in input are integers.
* 3 \leq n \leq 2 \times 10^5
* 2 \leq k \leq 10^9

Input

Input is given from Standard Input in the following format:


n k


Output

Print the number of possible combinations of numbers of people in the n rooms now, modulo (10^9 + 7).

Examples

Input

3 2


Output

10


Input

200000 1000000000


Output

607923868


Input

15 6


Output

22583772
#include <bits/stdc++.h>

#define ff first
#define ss second
#define pb push_back

using namespace std;
using ll = long long;
using ii = pair<int, int>;

const int N = 400005;
const int mod = 1e9 + 7;

ll fat[N];

ll expr(ll b, ll e){
	ll ans = 1;
	while(e){
		if(e&1){
			ans = (ans * b) % mod;
		}
		e >>= 1;
		b = (b * b) % mod;
	}
	return ans;
}

ll inv(ll b){
	return expr(b, mod-2);
}

ll C(int k, int n){
	return fat[n] * inv(fat[k] * fat[n-k] % mod) % mod;
}

int main() {
	fat[0] = 1;
	for(int i = 1; i < N; i++){
		fat[i] = (fat[i-1] * i) % mod;
	}
	int n, k;
	scanf("%d %d", &n, &k);
	ll ans = 0;
	for(int i = 0; i <= min(n-1, k); i++){
		ll aux = C(i, n);
		aux *= C(i, n-1);
		ans += aux;
		ans %= mod;
		//cerr << i << " " << n << " " << aux << endl;
	}
	printf("%lld\n", ans);
	return 0;
}
