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"
#define int long long

using namespace std;
int MOD = 1000000007;

int modpow(int a, int p){
    if(p == 0){
        return 1;
    }else if(p % 2 == 0){
        int t = modpow(a, p/2);
        return t * t % MOD;
    }else{
        int t = modpow(a, p/2);
        return t * t % MOD * a % MOD;
    }
}

int modinv(int n) { return modpow(n, MOD - 2); }

signed main() {
    int n, k;
    cin >> n >> k;
    k = min({k, n - 1});
    int ans = 0, fa = 1, fap = 1, ifa = 1;
    for(auto i = 0LL; i < k; i++){
        fa *= (n - i);
        fap *= (n - 1 - i);
        fa %= MOD;
        fap %= MOD;
        ifa *= modinv(i+1);
        ifa %= MOD;
        ans += fa * ifa % MOD * fap % MOD * ifa % MOD;
        ans %= MOD;
    }
    cout << ans + 1 << endl;

    return 0;
}