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 M 1000000007
#define cs ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
typedef long long ll;

using namespace std;
ll fac[200005];
ll power(ll x,ll y){
    ll t=1;
    while(y){
        if(y&1) t=(t*x)%M;
        y>>=1;
        x=(x*x)%M;
    }
    return t;
}
ll per(ll n,ll r){
    return (fac[n]*((power(fac[r],M-2)*power(fac[n-r],M-2))%M)%M);
}
void pre(){
    fac[0]=fac[1]=1;
    ll i=2;
    while(i<200003){
        fac[i]=(fac[i-1]*i)%M;
        i++;
    }
}
int main(){
    cs;
    pre();
    ll n,k,ans=0;
    cin>>n>>k;
    if(k>n-1) k=n-1;
    for(ll i=0;i<=k;i++) ans=(ans+per(n,i)*per(n-1,i))%M; 
    while(ans<0) ans+=M;
    cout<<ans;
}