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;

const long mod = 1000000007; 

long pmod(long b, long e) {
  if (e == 0) return 1;
  if (e % 2 == 1) return b * pmod(b, e - 1) % mod;
  long t = pmod(b, e / 2);
  return t * t % mod;
}

long inv(long n) {
  return pmod(n, mod - 2);
}


int n, k;
long f[800001];
void pre() {
  int max = n;
  f[0] = 1;
  for (int i = 1; i <= max; ++i) {
    f[i] = f[i - 1] * i % mod;
  }
}

long comb(long n, long r) {
  return f[n] * inv(f[n - r] * f[r] % mod) % mod; 
}

int main() {
  cin >> n >> k;
  k = min(k, n);
  pre();
  long sum = 0;
  for (int i = 0; i <= k; ++i) {
    sum = (sum + comb(n, i) * comb(n - 1, i)) % mod;
  }
  cout << sum << endl;
}