Problem:
Score : 500 points

Problem Statement

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).

Sample Input 1

3 2

Sample Output 1

10

Let c_1, c_2, and c_3 be the number of people in Room 1, 2, and 3 now, respectively. There are 10 possible combination of (c_1, c_2, c_3):

(0, 0, 3)

(0, 1, 2)

(0, 2, 1)

(0, 3, 0)

(1, 0, 2)

(1, 1, 1)

(1, 2, 0)

(2, 0, 1)

(2, 1, 0)

(3, 0, 0)

For example, (c_1, c_2, c_3) will be (0, 1, 2) if the person in Room 1 goes to Room 2 and then one of the persons in Room 2 goes to Room 3.

Sample Input 2

200000 1000000000

Sample Output 2

607923868

Print the count modulo (10^9 + 7).

Sample Input 3

15 6

Sample Output 3

22583772

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.*;

public class Main {

    public static void main(String[] args) {
        final long MOD = (long) (1e9) + 7;
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int k = sc.nextInt();

        long[] frac = new long[n + 1];
        long[] frac_inv = new long[n + 1];

        frac[0] = 1;
        frac_inv[0] = 1;
        for (int i = 1; i <= n; i++) {
            frac[i] = (frac[i-1] * i) % MOD;
            frac_inv[i] = modinv(frac[i], MOD);
        }

        k = Math.min(k, n - 1);

        long ans = 0;
        for (int j = 0; j <= k; j++) {
            long nCj = (frac[n] * frac_inv[j] % MOD) * frac_inv[n - j] % MOD;
            long pCq = (frac[n - 1] * frac_inv[n - j - 1] % MOD) * frac_inv[j] % MOD;
            ans = (ans + ((nCj * pCq) % MOD)) % MOD;
        }

        System.out.println(ans);
    }

    static long modpow(long a, long n, long MOD) {
        long res = 1;
        while (n > 0) {
            if ((n & 1) == 1) {
                res = (res * a) % MOD;
            }
            a = (a * a) % MOD;
            n >>= 1;
        }

        return res;
    }

    static long modinv(long a, long MOD) {
        return modpow(a, MOD - 2, MOD);
    }
}