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<iostream>
#include<algorithm>
#include<vector>
#include<queue>
#include<stack>
#include<string>
#include<map>
#include<tuple>
#include<cmath>


#define MOD 1000000007
#define rep(i,k,N) for(int i=k;i<N;i++)
#define MP make_pair
#define MT make_tuple //tie,make_tuple は別物
#define PB push_back

typedef long long ll;

using namespace std;

int dx[4]={1,0,-1,0};
int dy[4]={0,1,0,-1};

long long inv(long long x){
	long n=MOD-2,a=1;
	while(n>0){
		if(n%2) a=a*x%MOD;
		x=x*x%MOD;
		n=n/2;
	}
	return a;
}

int main(){
    int n,k;
    cin>>n>>k;
    ll ans = 1;
    ll r1=1, r2=1;

    rep(i,1,min(n,k+1)){
        r1 *= (n-i+1)*inv(i)%MOD;
        r1 %= MOD;
        r2 *= (n-i)*inv(i)%MOD;
        r2 %= MOD;
        ans += r1*r2 % MOD;
        ans %= MOD;
    }

    cout << ans;
    return 0;
}