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>
#define rep(i,n) for(int i=0; i<(int)(n); i++)

using namespace std;
typedef long long LL;
const LL mod=1e9+7;
const int Max_Num=200010;

LL modinv(LL x){
	LL m=mod, u=1, v=0;
	while(m){
		LL t=x/m;
		x-=t*m; swap(x,m);
		u-=t*v; swap(u,v);
	}
	u%=mod;
	if(u<0) u+=mod;
	return u;
}

int main(){
  LL n, k;
  cin >> n >> k;
  LL F[Max_Num], Finv[Max_Num];
  F[0]=1;
  rep(i,Max_Num-1){
  	F[i+1]=F[i]*(i+1);
  	F[i+1]%=mod;
  }
  rep(i,Max_Num) Finv[i]=modinv(F[i]);
  LL dp[Max_Num]={0};
  dp[0]=1;
  for(LL i=1; i<=min(k,n-1); i++){
    dp[i]=dp[i-1]+(F[n]*Finv[i]%mod*Finv[n-i]%mod)
    *(F[n-1]*Finv[n-i-1]%mod*Finv[i]%mod);
    dp[i]%=mod;
  }
  if(k<=n-1) cout << dp[k] << endl;
  else cout << dp[n-1] << endl;

  return 0;
}
