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 {
    private static final int MOD = 1_000_000_007;

    public static void main(final String[] args) {
        final Scanner scanner = new Scanner(System.in);
        final int n = scanner.nextInt();
        final int k = scanner.nextInt();

        final CombinationCalculator comb = new CombinationCalculator(2 * n, MOD).init();
        long sum = 0;
        for (int i = 0; i < Math.min(n, k + 1); i++) {
            sum += comb.calc(n, i) * comb.calc(n - 1, n - i - 1);
            sum %= MOD;
        }

        System.out.println(sum);
    }

    private static class CombinationCalculator {
        private final int size;
        private final int mod;
        private final long[] factorials;
        private final long[] invertedElements;
        private final long[] invertedFactorials;

        CombinationCalculator(final int size, final int mod) {
            this.size = size;
            this.mod = mod;
            this.factorials = new long[size];
            this.invertedElements = new long[size];
            this.invertedFactorials = new long[size];
        }

        CombinationCalculator init() {
            factorials[0] = 1;
            factorials[1] = 1;
            invertedFactorials[0] = 1;
            invertedFactorials[1] = 1;
            invertedElements[1] = 1;
            for (int i = 2; i < size; i++) {
                factorials[i] = factorials[i - 1] * i % mod;
                invertedElements[i] = mod - invertedElements[mod % i] * (mod / i) % mod;
                invertedFactorials[i] = invertedFactorials[i - 1] * invertedElements[i] % mod;
            }
            return this;
        }

        long calc(final int n, final int k) {
            return factorials[n] * (invertedFactorials[k] * invertedFactorials[n - k] % mod) % mod;
        }
    }
}
