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 {
	static final int r = 1000000000 + 7;
	static int n;
	static long fact[], finv[], inv[];
	
	public static void cominit() {
		fact = new long[n + 2];
		finv = new long[n + 2];
		inv = new long[n + 2];
		fact[0] = fact[1] = 1;
		finv[0] = finv[1] = 1;
		inv[1] = 1;
		for(int i = 2; i < n + 2; ++i) {
			fact[i] = (fact[i - 1] * i) % r;
			inv[i] = r - (inv[r % i] * (r / i)) % r;
			finv[i] = (finv[i - 1] * inv[i]) % r;
		}
	}
	
	public static int comb(int n, int k) {
		if(n < k)return 0;
		if(k < 0 || n < 0)return 0;
		if(k == 0)return 1;
		
		return (int)((fact[n] * (finv[k] * finv[n - k] % r)) % r);
	}

	public static int homogenerous(int x, int y) {
		return comb(x + y - 1, x - 1);
	}
	public static void main(String args[]) {
		Scanner sc = new Scanner(System.in);
		n = sc.nextInt();
		int k = sc.nextInt();
		cominit();
		sc.close();
		long ans = 0;
		int len = Math.min(n - 1, k);
		for(int i = 0; i <= len; ++i){
			long tmp = (long)comb(n, i) % (long)r;
			tmp *= (long)homogenerous(n - i, i);
			tmp %= (long)r;
			ans += tmp;
			ans %= (long)r;
		}
		System.out.println(ans);
	}
}