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 int MOD=1000000007;
const int MAX=2e5+9;

int n, k;
ll fact[MAX];

ll fastPow(ll a, ll b){
    if (!b) {
        return 1;
    }

    ll sq=fastPow(a, (b>>1LL));
    sq*=sq;

    if (b&1) {
        sq%=MOD;
        sq*=a;
    }

    return sq%MOD;
}

ll inv(ll a) {
    return fastPow(a, MOD-2);
}

ll C(ll n, ll k) {
    return fact[n]*inv(fact[k])%MOD*inv(fact[n-k])%MOD;
}

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

    cin >> n >> k;
    fact[0]=1;
    for (int i=1; i<=n; ++i) {
        fact[i]=fact[i-1]*i%MOD;
    }

    ll ans=0;
    for (int can=0; can<=min(n-1, k); ++can) {
        ans+=C(n, can)*C(n-can+(can-1), can)%MOD;
        ans%=MOD;
    }

    cout << ans;

    return 0;
}
