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 final int MOD = (int)1e9+7;
    
    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);
        
        int n = Integer.parseInt(sc.next());
        int k = Integer.parseInt(sc.next());
        
        Combination comb = new Combination((int)1e5*5, MOD);
        
        long ans = 0;
        for(int i=0; i<Math.min(k, n-1)+1; i++){
            long room = comb.c(n, i);
            long c = comb.h(n-i, i);
            long tmp = room*c%MOD;
            ans = (ans+tmp)%MOD;
        }
        
        System.out.println(ans);
    }
}

class Combination{
    int mod;
    long[] fact;
    long[] rfact;
    
    public Combination(int max, int mod){
        this.mod = mod;
        fact = new long[max];
        rfact = new long[max];
        fact[0] = 1;
        rfact[0] = 1;
        for(int i=1; i<max; i++){
            fact[i] = (fact[i-1]*i)%mod;
            rfact[i] = mod_inverse(fact[i], mod);
        }
    }
    
    public static long mod_pow(long x, long p, long m){
        long a = 1;
        while(p>0){
            if(p%2==1){
                a = a*x%m;
            }
            x = x*x%m;
            p /= 2;
        }
        return a;
    }
    
    public static long mod_inverse(long a, long m){
        return mod_pow(a, m-2, m);
    }
    
    public long p(int n, int r){
        if(r < 0 || n < r) return 0;
        return fact[n] * rfact[r]%mod;
    }
    
    public long c(int n, int r){
        if(r < 0 || n < r) return 0;
        return fact[n] * rfact[r]%mod * rfact[n-r]%mod;
    }
    
    public long h(int n, int r){
        if(n < 0 || r < 0) return 0;
        return r==0||n==0 ? 1 : c(n+r-1, r);
    }
}