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.Scanner;

public class Main {

    public static void main(String[] args) throws Exception {
        try (Scanner sc = new Scanner(System.in)) {
            long MOD = 1000000007;

            int N = sc.nextInt();
            int K = sc.nextInt();

            long[] fact = new long[N + 1];
            fact[0] = 1;
            for (int i = 1; i <= N; i++) {
                fact[i] = fact[i - 1] * i % MOD;
            }

            long ans = 0;
            for (int i = 0; i <= K; i++) {
                if (N - i <= 0) {
                    break;
                }

                ans = (ans + combination(fact, N, N - i, MOD) * combination(fact, N - 1, i, MOD)) % MOD;
            }

            System.out.println(ans);
        }
    }

    static long combination(long[] fact, int N, int K, long MOD) {
        long comb = fact[N];
        long factK = fact[K];
        long factM = fact[N - K];

        long m = MOD - 2;
        while (m > 0) {
            if (m % 2 == 1) {
                comb = comb * factK % MOD;
                comb = comb * factM % MOD;
                m--;
            }

            factK = factK * factK % MOD;
            factM = factM * factM % MOD;
            m = m / 2;
        }

        return comb;
    }

}
