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
import java.util.*;

public class Main {
    static final int MOD = 1000000007;
	public static void main (String[] args) {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int k = sc.nextInt();
		Combination cmb = new Combination(n * 2 + 1);
		long ans = 0;
		for (int i = 0; i <= Math.min(k, n - 1); i++) {
		    ans += cmb.getComb(n, i) * cmb.getComb(n - 1, i);
		    ans %= MOD;
		}
		System.out.println(ans);
   }

}

class Combination {
    static final int MOD = 1000000007;
    long[] fac;
    long[] finv;
    long[] inv;
    
    public Combination (int size) {
        fac = new long [size];
        finv = new long [size];
        inv = new long [size];
        fac[0] = 1;
        fac[1] = 1;
        finv[0] = 1;
        finv[1] = 1;
        inv[1] = 1;
        for (int i = 2; i < size; i++) {
            fac[i] = fac[i - 1] * i % MOD;
            inv[i] = MOD - inv[MOD % i] * (MOD / i) % MOD;
            finv[i] = finv[i - 1] * inv[i] % MOD;
        }
    }
    
    
    public long getComb(int n, int k) {
        if (n < k || n < 0 || k < 0) {
            return 0;
        }
        return fac[n] * (finv[k] * finv[n - k] % MOD) % MOD;
    }
    
}

