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>
#pragma GCC target("avx2")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
using namespace std;
typedef long long ll;
const ll mod  = 1000000007;
ll modinv(ll a){
  ll b = mod,u = 1,v = 0,t;
  while(b){
    t = a/b;
    a -= t*b;swap(a,b);
    u -= t*v;swap(u,v);
  }
  u %= mod;
  if(u < 0) u += mod;
  return u;
}
int main(){
  ll n,k,i,ans = 0;scanf("%lld%lld",&n,&k);
  ll P[n+1];P[0] = P[1] = 1;
  for(i=2;i<=n;i++) P[i] = P[i-1]*i%mod;
  for(i=0;i<min(n,k+1);i++){
    ans = (ans+P[n]*modinv(P[i])%mod*modinv(P[n-i])%mod*P[n-1]%mod*modinv(P[n-i-1])%mod*modinv(P[i])%mod)%mod;
  }
  printf("%lld\n",ans);
}