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<ll,ll> pll;

ll mod=1e9+7;

ll mpow(ll x, ll n) {
  ll ans=1;
  while(n>0) {
    if(n&1) {
      ans=ans*x%mod;
    }
    x=x*x%mod;
    n>>=1;
  }
  return ans;
}

//階乗
vector<ll> tfact(1e7+1);
void fact(ll n) {
  for(ll i=0;i<=n;i++) {
    if(i==0) {
      tfact[i]=1;
    }
    else {
      tfact[i]=tfact[i-1]*i%mod;
    }
  }
}

//nCk
ll comb(ll n, ll k) {
  return tfact.at(n)*mpow(tfact.at(k),mod-2)%mod*mpow(tfact.at(n-k),mod-2)%mod;
}

int main() {
  ll n,k;
  cin >> n >> k;
  fact(n);
  k=min(k,n-1);
  ll ans=1;
  for(ll i=1;i<=k;i++) {
    ll temp=comb(n,i);
    ans=(ans+comb(i+n-i-1,i)*temp%mod)%mod;
  }
  cout << ans << endl;
}