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 long long ll;
#define rep(i,a) for(int i=0;i<(a);i++)
const ll MOD=1000000007;
//const ll MOD=998244353;

const int MAX_N=202020;
ll inv[MAX_N+1], fact[MAX_N+1], ifact[MAX_N+1];

ll comb(int n, int k){
  if(n<k) return 0;
  return fact[n]*ifact[k]%MOD*ifact[n-k]%MOD;
}

void prepare(){
  inv[1]=fact[0]=fact[1]=ifact[0]=ifact[1]=1LL;
  for(int i=2;i<=MAX_N;i++){
    inv[i]=inv[MOD%i]*(MOD-MOD/i)%MOD;
    fact[i]=fact[i-1]*i%MOD;
    ifact[i]=ifact[i-1]*inv[i]%MOD;
  }
}


int main(){
  cin.tie(0);
  ios::sync_with_stdio(false);
  
  prepare();
  int N,K; cin>>N>>K;
  ll ans=1+1LL*N*(N-1);
  for(int i=2;i<=min(N-1,K);i++){
    (ans+=comb(N,i)*comb(N-1,i)%MOD)%=MOD;
  }
  cout<<ans<<endl;
  return 0;
}