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 {

    // global
    static long fact[];
    static long inverse[];
    static int mod = 1_000_000_007;

    static long pow(long a,int n) {
        long res=1;
        while (n>0) {
            if ((n-n/2*2)==1) {
                res=res*a%mod;
            }
            a=a*a%mod;
            n>>=1;
        }
        return res;
    }

    static long modinv(long n) {
        return pow(n, mod-2);
    }

    static long comb(int n,int k){
        if(n<0 || k<0 || n<k)return 0;
        return fact[n]*(inverse[k]*inverse[n-k]%mod) %mod;
    }

    public static void main(String[] args) {
        // main method
        fact=new long[500000];
        fact[0]=1;
        inverse=new long[500000];
        inverse[0]=1;
        for(int i=1;i<500000;i++){
            fact[i]=(fact[i-1]*(long)i)%mod;
            inverse[i]=modinv(fact[i]);
        }
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int k = sc.nextInt();
        if (k>=n-1) {
            System.out.println(comb(n+n-1, n-1));
            return;
        }
        long ans = 0L;
        for (int i=0;i<=k;i++) {
            ans = (ans+comb(n, i)*comb(n-(n-i)+(n-i)-1, n-i-1)%mod)%mod;
        }
        System.out.println(ans);
    }
}