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 unsigned long long ULL;
const int nMax=1e6+1, MOD=1e9+7;
ULL inv[nMax], Fact[nMax], invF[nMax];
ULL Comb(int n, int r){ return (((Fact[n]*invF[r])%MOD)*invF[n-r])%MOD; }

ULL Ans(int n, int x){
ULL N=n;
if(x==0){ return 1; }
if(x>=n){ return Ans(n, n-1); }
else{ return (Ans(n, x-1)+(Comb(n, x)*Comb(n-1, n-x-1))%MOD)%MOD; } 
}

int main(){
int n, k;
inv[1]=Fact[0]=Fact[1]=invF[0]=invF[1]=1;
for(int i=2; i<nMax; i++){ 
  inv[i]=((MOD-MOD/i)*inv[MOD%i])%MOD;
  Fact[i]=(Fact[i-1]*i)%MOD; invF[i]=(invF[i-1]*inv[i])%MOD;
}
cin >> n >> k;  
cout << Ans(n, k) << "\n";
}