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;

const ll mod = 1e9+7;
const int N = 4e5;

ll iv[N+1], f[N+1], f2[N+1];

ll nck(ll n, ll k){
    return f[n]*f2[n-k]%mod*f2[k]%mod;
}

int main() {
    ios::sync_with_stdio(0);
    cin.tie(0);
    ll n, k;
    cin >> n >> k;
    iv[1] =1;
    for(ll i=2; i<=N; i++)
        iv[i] =mod-mod/i*iv[mod%i]%mod;
    f[0]=f2[0]=1;
    for(ll i=1; i<=N; i++){
        f[i] =i*f[i-1]%mod;
        f2[i] = iv[i] *f2[i-1] %mod;
    }
    ll ans = nck(2*n-1, n-1)%mod;
    for(ll i=k+1; i<n; i++){
        ans += 2*mod;
        ans -= (nck(n, i)*nck(n-1, n-i-1))%mod;
        ans %= mod;
    }
    cout << ans%mod;
    return 0;
}
