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>
#include<vector>
#include<math.h>
using namespace std;
long long pow2(long long x,int y,long long mod) {
  if(y == 0)return 1;
  else if(y%2 == 0)return (long long)powl(pow2(x,y/2,mod),2.0)%mod;
  else return (((long long)powl(pow2(x,y/2,mod),2.0)%mod)*x)%mod;
}
int main() {
  int N,K;
  cin >> N >> K;
  long long ans = 0;
  vector<long long> f(N+1),fi(N+1);
  f[0] = 1;
  int i;
  for(i=0;i<N;i++)f[i+1] = f[i]*(i+1)%1000000007;
  for(i=0;i<=N;i++)fi[i] = pow2(f[i],1000000005,1000000007);
  for(i=0;i<=min(N-1,K);i++) {
    ans += (fi[i]*fi[i]%1000000007)*(fi[N-i]*fi[N-i-1]%1000000007)%1000000007;
    ans %= 1000000007;
  }
  ans = ans * (f[N]*f[N-1]%1000000007) % 1000000007;
  cout << ans%1000000007 << endl;
}