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;

long inv(int a, int m) {
    long i = 1, j = 0;
    for(int b = m; a > 1; swap(i, j), swap(a, b)) {
        j = (j + b / a * (m - i)) % m;
        b %= a;
    }
    return i;
}
long f[222222] = {1};
long co(long a, long b, int p) {
    return f[a] * inv(f[b] * f[a - b] % p, p) % p;
}
int main() {
    int n, k, p = 1e9 + 7;
    cin >> n >> k;
    for(int i = 0; i < n; i++)
        f[i + 1] = f[i] * (i + 1) % p;
    k = min(k, n - 1);
    long r = 0;
    for(int i = n - k; i <= n; i++)
        (r += co(n, i, p) * co(n - 1, i - 1, p) % p) %= p;
    cout << r << endl;
    return 0;
}
