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;
static const int64_t mod=1000000007;
using ll=long long ;
ll f(ll x,ll y){
if(y==0) return 1;
  else{
  if(y%2==0)
  return (f(x,y/2)*f(x,y/2))%mod;
   else
  return (((x*f(x,y/2))%mod)*f(x,y/2))%mod;
 
  }
 
}
int main(){
ll n,k;
  cin>>n>>k;
  if(k<=n-1){
  vector<ll>A(k+1);
    A.at(0)=1;
    for(int i=1;i<=k;i++)
    A.at(i)=(((A.at(i-1)*(n-i))%mod)*(((n-i+1)*f(i,2*mod-4))%mod))%mod;
      int64_t ans=0;
      for(int i=0;i<=k;i++)
        ans=(ans+A.at(i))%mod;
      cout<<ans<<endl;
    
  
  }else{
  vector<ll>A(n);
    A.at(0)=1;
    for(int i=1;i<n;i++)
    A.at(i)=(((A.at(i-1)*(n-i))%mod)*(((n-i+1)*f(i,2*mod-4))%mod))%mod;
      int64_t ans=0;
      for(int i=0;i<n;i++)
        ans=(ans+A.at(i))%mod;
      cout<<ans<<endl;
  }
   return 0;
}