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>
using namespace std;
const int mod = 1e9 + 7;
const int maxn = 4e5 + 10;
long long a[maxn];
long long pow_mod(long a, long n) {
    long long ret = 1;
    while (n) {
        if (n & 1) ret = ret * a % mod;
        a = a * a % mod;
        n >>= 1;
    }
    return ret;
}

void init() {
    a[0] = 1;
    for (int i = 1; i < maxn; i++) {
        a[i] = a[i - 1] * i % mod;
    }
}

long long Cc(long long x, long long y) {
    return a[x] * pow_mod(a[y] * a[x - y] % mod, mod - 2) % mod;
}

int main() {
    init();
    long long n, k, ans;
    cin >> n >> k;

    ans = Cc(2 * n - 1, n);
    for (int i = 1; i <= n - k - 1; i++) ans = (ans - Cc(n, i) * Cc(n - 1, i - 1) % mod) % mod;
    cout << (ans % mod + mod) % mod << endl;
}