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>

#define rep(i, n) for(int i=0; i < n; i++)
#define reps(i, n) for(int i=1; i <= n; i++)
#define INF 1e9
#define ALL(v) v.begin(), v.end()

using namespace std;
using ll=long long;

ll mod = 1000000007;

ll modpow(ll a,ll n,ll mod){
  ll res=1;
  while(n>0){
    if(n & 1)res=res*a%mod;
    a =a*a%mod;
    n>>=1;
  }
  return res;
}

int main(){
  ll n,k;
  ll ans=1;
  ll c1=1;
  ll c2=1;
  cin >> n >> k;
  
  k= min(k,n-1);

  reps(i,k){
    c1 = (c1*(n-i+1))%mod;
    c1 = (c1*modpow(i,mod-2,mod))%mod;
    c2 = (c2*(n-i))%mod;
    c2 = (c2*modpow(i,mod-2,mod))%mod;
    ans += (c1*c2)%mod;
    ans %= mod;
  }
  cout << ans;
}