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 ll;
typedef pair<int,int> P;
#define rep(i,m,n) for(int i=m;i<n;i++)
ll mod=1e9+7;

ll power(ll x,ll n){
    if(n==0) return 1;
    ll res=power(x*x%mod,n/2);
    if(n&1) res=res*x%mod;
    return res;
}

int main(){
  int n;
  ll k;
  cin>>n>>k;
  ll a[n+1];
  a[0]=1;
  rep(i,1,n+1) a[i]=a[i-1]*i%mod;
  ll b[n+1];
  b[0]=1;
  rep(i,1,n+1) b[i]=power(a[i],1e9+5);
  int p;
  if(n-1<=k) p=n-1;
  else p=k;
  ll ans=0;
  rep(i,0,p+1){
    ans+=(a[n]*b[i]%mod*b[n-i]%mod)*(a[n-1]*b[i]%mod*b[n-1-i]%mod)%mod;
    ans%=mod;
  }
  if(p==1) ans--;
  cout<<ans<<endl;
}