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>
#include<iomanip>
#define ll long long
#define pb push_back
#define mp make_pair
#define MOD 1000000007
using namespace std;

ll fact[500005];

ll p(ll x, ll n) {
	ll res=1;
	while(n) {
		if(n&1) res=(res*x)%MOD;
		x=(x*x)%MOD;
		n/=2;
	}
	return res;
}

ll nCr(ll n, ll r) {
	ll ans=1,i;
	//ll cut=(n-r);
	//for(i=n;i>n-r;i--) ans=(ans*i)%MOD;
	ans = (ans*fact[n])%MOD;
	ans = (ans*p(fact[r],MOD-2))%MOD;
	ans=(ans*p(fact[n-r],MOD-2))%MOD;
	return ans;
}

int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    
    ll n,k,x,i,sum=0;
    cin >> n >> k;
    fact[0]=1;
    for(i=1;i<500005;i++) fact[i]=(fact[i-1]*i)%MOD;
    for(x=0;x<=min(n-1,k);x++) sum=(sum+(nCr(n-1,x)*nCr(n,x))%MOD)%MOD;
    cout << sum << "\n";
    return 0;
}

