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 rep(i,n) for(int i=0;i<n;i++)
#define all(v) v.begin(), v.end()
typedef long long ll;
typedef pair<ll,ll> P;
typedef vector<ll> vec;
typedef vector<vec> mat;
ll n,k;
ll mod=1e9+7;
ll inv(ll a){
    ll n=mod-2,ans=1;
    while(n>0){
        if(n&1) ans=ans*a%mod;
        n=n/2;
        a=a*a%mod;
    }
    return ans;
}
ll A[400001];
void init(){
    A[0]=1;
    rep(i,400000) A[i+1]=A[i]*(i+1)%mod;
}
ll nCk(ll n,ll k){
    return A[n]*inv(A[k])%mod*inv(A[n-k])%mod;
}
int main(){
    init();
    cin>>n>>k;
    if(k>=n) k=n-1;
    ll ans=0;
    rep(i,k+1) ans=(ans+nCk(n-1,i)*nCk(n,i)%mod)%mod;
    cout<<ans;
}