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 <cstdio>
#include <algorithm>
using namespace std;
#define ll long long
ll mod = 1000000007;
ll big(ll b, ll p){
	if (p == 1) return b;
	ll h = big(b, p / 2);
	ll res = (h * h) % mod;
	if (p % 2 == 1) res = (res * b) % mod;
	return res;
}
int main(){
	ll n, k, c1 = 1, c2 = 1, ans = 1;
	scanf("%lld %lld", &n, &k);
	for (int i = 1; i <= min(n - 1, k); i++){
		c1 = (c1 * (n + 1 - i)) % mod;
		c1 = (c1 * big(i, mod - 2)) % mod;
		c2 = (c2 * (n - i)) % mod;
		c2 = (c2 * big(i, mod - 2)) % mod;
		ans += (c1 * c2) % mod;
		ans %= mod;
	}
	printf("%lld\n", ans);
}