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.*;

class Main {
	Scanner sc;
	int n, k;
	static final int MOD = 1_000_000_007;
	
	void calc() {
		sc = new Scanner(System.in);
		n = sc.nextInt();
		k = Math.min(n, sc.nextInt());
		
		long s = 1;
		long f = 1;
		long nCi = 1;
		for (int i = 1; i <= k; i++) {
			f = f * (n-i) % MOD * inv(i) % MOD;
			nCi = nCi * (n-i+1) % MOD * inv(i) % MOD;
			s = (s + nCi * f % MOD) % MOD;
		}
		System.out.println(s);
	}
	
	static final long inv(long a) {
		long b = MOD;
		long aa = a, bb = b;
		long x0 = 1, x1 = 0;
		long y0 = 0, y1 = 1;
	
		while (b != 0) {
			long q = a / b;
			long r = a % b;
			long x2 = x0 - q * x1;
			long y2 = y0 - q * y1;
	
			a = b; b = r;
			x0 = x1; x1 = x2;
			y0 = y1; y1 = y2;
		}
		if (bb > 0 && x0 < 0) {
			long n = -x0/bb;
			if (-x0%bb != 0) n++;
			x0 += n*bb; y0 -= n*aa;
		}
	    return x0;
	}
	
	public static void main(String[] args) {
		new Main().calc();
	}
}