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;
using ll = long long;

const ll mod = 1000000007;

int power(ll a, ll b=mod-2){
  ll res=1;
  while(b>0){
   if(b & 1) res=res*a%mod;
    a=a*a%mod;
    b>>=1;
  }
  
  return res;
  
}

int main(){
  ll n,k; 
  cin >> n >> k;
  k=min(k,n-1);
  vector<ll>fact1(n+1),fact2(n+1);
  fact1[0]=1;
  for(int i=1; i<=n; i++) fact1[i]=fact1[i-1]*i,fact1[i]%=mod;
  fact2[n]=power(fact1[n]);
  for(int i=n; i>=1; i--) fact2[i-1]=fact2[i]*i,fact2[i-1]%=mod;
  
  ll ans = 0;
  for(int i=0; i<=k; i++){
    ll x=1;
    x*=fact1[n];
    x%=mod;
    x*=fact1[n-1];
    x%=mod;
    x*=fact2[i];
    x%=mod;
    x*=fact2[i];
    x%=mod;
    x*=fact2[n-i];
    x%=mod;
    x*=fact2[n-i-1];
    ans+=x;
    ans%=mod;
  }
  
  cout << ans << endl; 
  
}
  
  
