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<cstdio>

const int MOD = 1000000007;
int f[200005], fi[200005];

int pow(int x, int y) {
  if (y == 0) {
    return 1;
  }
  if (y % 2 == 0) {
    return pow(1ll * x * x % MOD, y / 2);
  } else {
    return 1ll * x * pow(x, y - 1) % MOD;
  }
}

int nCr(int n, int r) {
  return ((1ll * f[n] * fi[r]) % MOD * fi[n-r]) % MOD;
}

int n, k;

int main() {
  f[0] = 1;
  for (int i = 1; i <= 200000; i++) {
    f[i] = 1ll * f[i - 1] * i % MOD;
  }
  fi[200000] = pow(f[200000], MOD - 2);
  for (int i = 199999; i >= 0; i--) {
    fi[i] = 1ll * fi[i + 1] * (i + 1) % MOD;
  }
  scanf("%d %d", &n, &k);
  if (k > n - 1) {
    k = n - 1;
  }
  int res = 0;
  for (int i = 0; i <= k; i++) {
    res += 1ll * nCr(n, i) * nCr(n - 1, i) % MOD;
    res %= MOD;
  }
  printf("%d\n", res);
}
