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;
#define long long long

const int MAX = 1e6;
const int MOD = 1e9+7;
long fac[MAX],finv[MAX],inv[MAX];

void combinit(){
    fac[0] = fac[1] = 1;
    finv[0] = finv[1] = 1;
    inv[1] = 1;
    for(int i = 2; i < MAX; ++i){
        fac[i] = fac[i-1]*i % MOD;
        inv[i] = MOD-inv[MOD%i] * (MOD/i) % MOD;
        finv[i] = finv[i-1]*inv[i] % MOD;
    }
}

long com(int n, int k){
    if(n < k) return 0;
    if(n < 0 or k < 0) return 0;
    return fac[n] * (finv[k] * finv[n-k] % MOD) % MOD;
}

int main(){
  combinit();
  int n, k;
  cin >> n >> k;
  long ans =0;
  for(int i=0; i<min(n, k+1); i++){
    ans = (ans+com(n,i)*com(n-1, n-i-1))%MOD;
  }
  cout << ans << endl;
  return 0;
}