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.math.BigInteger;
import java.util.Scanner;

public class Main {
	static long MOD = 1000000007;
	static BigInteger BMOD = new BigInteger(Long.toString(MOD));

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int k = sc.nextInt();
		long NINV = (new BigInteger(Integer.toString(n))).modInverse(BMOD).longValue();

		long combi = 1;
		long ans = 1;
		for ( int i = 0 ; i < Math.min(n - 1, k) ; i++ ) {
			combi = (combi * (n - i)) % MOD;
			combi = (combi * (new BigInteger(Integer.toString(i + 1))).modInverse(BMOD).longValue()) % MOD;

			long h = (combi * (n - i - 1)) % MOD;
			h = (h * NINV) % MOD;

			long p = (combi * h) % MOD;
			ans = (ans + p) % MOD;
		}

		System.out.println(ans);
	}
}
