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: Wrong Answer)

import java.util.*;
import java.io.PrintWriter;
public class Main{
	static long[] fact;
	static long[] inv;
	static long mod=1000000007;
	public static void main(String[] args){
		Scanner sc=new Scanner(System.in);
		int n=sc.nextInt();
		int k=sc.nextInt();
		fact=new long[2*n+1];
		fact[0]=1;
		fact[1]=1;
		for(int i=2; i<=2*n; i++){
			fact[i]=(fact[i-1]*i)%mod;
		}
		inv=new long[2*n+1];
		inv[2*n]=pow(fact[2*n],mod-2);
		for(int i=2*n-1; i>=0; i--){
			inv[i]=(inv[i+1]*(i+1))%mod;
		}
		long ans=comb(n+n-1,n-1);
		if(n-1<=k){
			System.out.println(ans);
		}else{
			ans=(ans-comb(n,n-1-k)*comb(k+n-2-k,n-2-k)+mod)%mod;
			System.out.println(ans);
		}
	}
	static long comb(int t,int y){
		long re=1;
		re*=fact[t];
		re*=inv[y];
		re%=mod;
		re*=inv[t-y];
		return re%mod;
	}
	static long pow(long p,long q){
		long res=1;
		while(q>0){
			if((q & 1)==1){
				res*=p;
				res%=mod;
			}
			q>>=1;
			p*=p;
			p%=mod;
		}
		return res;
	}

}