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;
int n,k;
const long long Mod = 1e9+7;
long long G[200001];
long long power(long long n,long long x)
{
    if(x==0)
        return 1;
    if(x&1)
        return n*power(n*n%Mod,x/2)%Mod;
    return  power(n*n%Mod,x/2);
}
long long nck(int n,int k)
{
    return G[n] *(power(G[k]*G[n-k]%Mod,Mod-2))%Mod;
}
long long res = 0;
int main()
{
    cin>>n>>k;
    G[0]=1;
    for(int i=1;i<=n;i++)
    {
        G[i]=G[i-1]*i%Mod;
    }
    for(int x = 0 ; x<=min(k,n-1);x++)
    {
        res += nck(n-1,n-x-1) * nck(n,x)%Mod;
        res%=Mod;
    }
    cout<<res;
    return 0;
}
