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;
typedef long long int ll;
typedef pair<ll,ll> p2;
ll p[200005],inv[200005],hell=pow(10,9)+7;
ll exp(ll x,ll y){
    ll res=1;
    while(y>0){
        if(y&1)
        res=(res*x)%hell;
        y>>=1;
        x=(x*x)%hell;
    }
    return res;
}
ll bin(ll n,ll r){
    ll res=p[n];
    res*=inv[n-r];
    res%=hell;
    res*=inv[r];
    res%=hell;
    return res;
}
int main(){
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    cout.tie(NULL);
    ll n,k,res=0;
    cin>>n>>k;
    p[0]=1;
    inv[0]=1;
    for(ll i=1;i<200005;i++){
        p[i]=(i*p[i-1])%hell;
        inv[i]=exp(p[i],hell-2);
    }
    for(ll i=0;i<min(k+1,n);i++){
        res+=(bin(n,i)*bin(n-1,i))%hell;
        res%=hell;
    }
    cout<<res;
}
