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.Scanner;
public class Main{
  public static void main(String[] args){
	Scanner sc = new Scanner(System.in);
    long n = sc.nextLong();
    long a = sc.nextLong();
    long b = sc.nextLong();
    long scoreA=0, scoreB=0;
    long score = 0;
    long before = 1;
    
    for(int i=1; i<=a; i++){
    	score = before * (a-i+1)/i;
        before = score;
    }
    scoreA = score;
    score =0; before = 1;
    for(int i=1; i<=b; i++){
    	score = before * (b-i+1)/i;
        before = score;      
    }
    long x = (long)Math.pow(2,n) - 1;
    long ans = x - (scoreA + scoreB) % 1000000007;
    System.out.println(ans);
  
  }
}