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 <iostream>
#include <algorithm>
#include <cstring>
using namespace std;
typedef long long LL;
const LL N = 1000000007;

LL fac[500005],inv[500005];

LL kpw(LL x,LL y){
	LL ans = 1,tmp = x;
	while(y){
		if(y & 1) ans = (ans * tmp) % N;
		tmp = (tmp * tmp) % N;
		y >>= 1;
	}
	return ans;
}

LL comb(LL x,LL y){
	return (((fac[x] * inv[y]) % N) * inv[x - y]) % N;
}

void init(){
	fac[0] = 1; for(LL i = 1;i <= 500000;i ++) fac[i] = (fac[i - 1] * i) % N;
	for(LL i = 0;i <= 500000;i ++) inv[i] = kpw(fac[i],N - 2);
}

int main() {
	LL n,k,ans = 0; init();
	cin >> n >> k;
	if(k >= n) k = n - 1;
	for(LL i = 0;i <= k;i ++) ans = (ans + (comb(n,i) * comb(n - 1,i)) % N) % N;
	cout << ans << endl;
	return 0;
}