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 Java7 (OpenJDK 1.7.0) (judge verdict: Wrong Answer)

import java.lang.Math;
import java.util.Scanner;
 
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 ans;

        ans = (long)(Math.pow(2,n)-combi(n,a)-combi(n,b)-1);
        ans = ans % 1000000007;

        System.out.print(ans);
    }

    public static long combi(long a,long b){
        long x=1;
        for(long i = 0 ; i<b ; i++){
            x = x*(a-i);
        }
        for(long i = b ; i<a ; i++){
            x = x/(a-i);
        }
        return x;
    }
}