Problem:
Score : 400 points

Problem Statement

Akari has n kinds of flowers, one of each kind.

She is going to choose one or more of these flowers to make a bouquet.

However, she hates two numbers a and b, so the number of flowers in the bouquet cannot be a or b.

How many different bouquets are there that Akari can make?

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

Here, two bouquets are considered different when there is a flower that is used in one of the bouquets but not in the other bouquet.

Constraints

All values in input are integers.

2 \leq n \leq 10^9

1 \leq a < b \leq \textrm{min}(n, 2 \times 10^5)

Input

Input is given from Standard Input in the following format:

n a b

Output

Print the number of bouquets that Akari can make, modulo (10^9 + 7). (If there are no such bouquets, print 0.)

Sample Input 1

4 1 3

Sample Output 1

7

In this case, Akari can choose 2 or 4 flowers to make the bouquet.

There are 6 ways to choose 2 out of the 4 flowers, and 1 way to choose 4, so there are a total of 7 different bouquets that Akari can make.

Sample Input 2

1000000000 141421 173205

Sample Output 2

34076506

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

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.*;

public class Main {
	public static void main(String[] args) {
		Scanner scan = new Scanner(System.in);
		
		long n = scan.nextLong();
		long a = scan.nextLong();
		long b = scan.nextLong();
		long ans = (long)Math.pow(2, n)-1;
		long mod = (long)Math.pow(10, 9)+7;
		
		ans -= calcNumOfCombination(n, a);
		ans -= calcNumOfCombination(n, b);
	
		ans = ans%mod;
		System.out.println(ans);
		
		
		
	}
	
	public static long calcNumOfCombination(long n,long r){
        long  num = 1;
        for(int i = 1; i <= r; i++){
            num = num * (n - i + 1) / i;
        }
        
        System.out.println(num);
        return num;
    }
}