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>

using namespace std;

typedef long long	ll;

const int N = int(2e5) + 10;
const ll mod = ll(1e9) + 7LL;

ll fat[N];

ll fast_expo(ll base, ll x, ll mod){
	ll r = 1LL;

	while(x){
		if(x & 1LL){
			r = (r * base) % mod;
		}

		base = (base * base) % mod;
		x >>= 1LL;
	}

	return r;
}

ll comb(ll n, ll k){
	ll inv1 = fast_expo((fat[k] * fat[n - k]) % mod, mod - 2, mod);

	return (fat[n] * inv1) % mod;
}

int main(){
	ll n, k;

	scanf("%lld %lld", &n, &k);

	fat[0] = 1LL;

	for(ll i = 1 ; i < N ; i++){
		fat[i] = (i * fat[i - 1]) % mod;
	}

	ll sum = 0LL;

	k = min(k, n - 1);

	for(int d = 0 ; d <= k ; d++){
		sum += (comb(n - 1, n - d - 1) * comb(n, d)) % mod;
		// printf("%lld\n", sum);

		if(sum >= mod){
			sum -= mod;
		}
	}

	printf("%lld\n", sum);

	return 0;
}