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 pi 3.14159265359
#define int long long
#define pii pair<int,int>
const int mod=1e9+7;
 
int dx[]={-1,0,1,0};
int dy[]={0,-1,0,1};

int power(int x,int p)
{
   int res=1;
   while(p)
   {
      if(p&1)res=(res*x)%mod;
      p=p>>1;
      x=(x*x)%mod;
   }
   return res;
}
vector<int>f(2e5+5),inv(2e5+5);
int ncr(int n,int r)
{
   return ((f[n]*inv[n-r])%mod*inv[r])%mod;
}


int32_t  main()
{ 
  ios::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
 

   
int n,k;
cin>>n>>k;

inv[0]=inv[1]=f[0]=f[1]=1;

for(int i=2;i<=f.size()-1;i++)
{
   f[i]=(f[i-1]*i)%mod;
   inv[i]=power(f[i],mod-2);
}
int ans=0;




for(int i=0;i<=min(n-1,k);i++)
{
    ans=(ans+(ncr(n,i)*ncr(n-1,i))%mod )%mod;
}
cout<<ans<<"\n";




}

