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 <iostream>
#include <cstdio>
#define N 2000005
using namespace std;

typedef long long ll;
ll n, k, ans, M = 1e9 + 7;
ll fac[N]={1,1}, inv[N]={1,1}, fiv[N]={1,1};
ll c(ll p, ll q) {return fac[p] * fiv[p-q] % M * fiv[q] % M;}

int main()
{
	ll i, j, t;
	cin >> n >> k;
	k = min(n, k);
	for(i=2; i<=n; i++) {
		fac[i] = fac[i-1] * i % M;
		inv[i] = inv[M%i] * (M-M/i) % M;
		fiv[i] = fiv[i-1] * inv[i] % M;
	}
	for (i = 0; i <= k; i++) {
		t = (c(n, i) * c(n - 1, i)) % M;
		ans = (ans + t) % M;
	}
	cout << ans << endl;
    return 0;
}
