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;

#define endl '\n'
typedef long long ll;
ll const M = 1000000007, N = 2e5 + 1;
ll f1[N], f2[N], iv[N];

ll mult(ll a, ll b){ return ( a%M * (b%M))%M;}
ll nck(ll n, ll k){
    return f1[n]*f2[n-k]%M*f2[k]%M;
}

int main(){
    ios_base::sync_with_stdio(false);
    cin.tie(0);

    iv[1] = f1[0] = f2[0] = 1;
    for (ll i=2; i<N; i++) iv[i] = (M - (M/i) * iv[M%i] % M) % M;
    for (ll i=1; i<N; i++){
        f1[i] = f1[i-1]*i%M;
        f2[i] = f2[i-1]*iv[i]%M;
    }

    ll n,k; cin >> n >> k;
    k = min(n-1, k);

    ll ans = 0;
    for (ll x=0; x <= k; x++){
        ans = (ans + nck(n, x) * nck(n-1, x)%M)%M;
    }
    cout << ans << endl;
}