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 inf = 0x3f3f3f3f;
const int maxn = 2e5 + 7;
const int mod = 1e9 + 7;
ll fc[maxn],f[maxn];

ll qpow(ll a,ll b){
	ll s = 1;
	a %= mod;
	while(b){
		if(b & 1) s = (s % mod) * (a % mod) % mod;
        b >>= 1;
        a = (a % mod) * (a % mod) % mod;
	}
	s %= mod;
	return s;
}

ll c(ll x,ll y){
	return fc[x]*qpow(fc[y]*fc[x-y]%mod,mod-2)%mod;
}
int main(){
	fc[0] = 1;
	for(int i = 1;i < maxn;i++)
		fc[i] = (fc[i-1]*i % mod);
	ll n,k;
	cin >> n >> k;
	f[1] = 1;
	for(int i = 2;i < maxn;i++)
		f[i] = (f[i-1]*i%mod);
	ll sum = 0;
	for(ll i = 0;i <= min(n,k);i++){
		sum += (c(n,i)*c(n-1,n-i-1)) % mod;
		sum %= mod;
	}
	cout << (sum + mod) % mod;
	return 0;
}