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>
#define ll long long
#define MOD 1000000007

using namespace std;

ll p[200001];

ll modinv(ll a, ll m = MOD) {
  ll b = m, u = 1, v = 0;
  while(b) {
    ll t = a / b;
    a -= t * b;
    swap(a, b);
    u -= t * v;
    swap(u, v);
  }
  u %= m;
  if(u < 0) u += m;
  return u;
}

ll cmb(ll n, ll r) {
  return p[n] * modinv(p[r]) % MOD * modinv(p[n - r]) % MOD;
}

int main() {
  p[0] = 1;
  for(int i = 1; i < 200001; i++) p[i] = (p[i - 1] * i) % MOD;
  ll n, k, o = 1;
  scanf("%lld %lld", &n, &k);
  for(int i = 1; i <= min(k, n - 1); i++)
    o = (o + cmb(n, i) * cmb(n - 1, i) % MOD) % MOD;
  printf("%lld\n", o);
}