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 ll long long
#define inf 1000000007
using namespace std;
ll a[200009],b[200009];
ll pow1(ll x,ll y)
{
    ll res=1;
    while(y)
    {
        if(y%2)
            res=res*x%inf;
        x=x*x%inf;
        y/=2;
    }
    return res;
}
int main()
{
    ll n,k,ans=0;
    scanf("%lld%lld",&n,&k);
    a[0]=1,b[0]=1;
    for(int i=1;i<=n;i++)
        a[i]=a[i-1]*(ll)(i)%inf,b[i]=b[i-1]*pow1((ll)i,inf-2)%inf;
    for(int i=1;i<=min(n-1,k);i++)
        ans=(ans+a[n]*b[i]%inf*b[n-i]%inf*a[n-1]%inf*b[i]%inf*b[n-i-1]%inf)%inf;
    if(k>=2)
        ans=(ans+1)%inf;
    printf("%lld",ans);
    return 0;
}
