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 {

    static final int MOD=1000000007;


    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n=sc.nextInt();
        int a = sc.nextInt();
        int b=sc.nextInt();
        long ans = 1;

        for(int i=0;i<n;i++){
            ans*=2;
            ans%=MOD;
        }
        ans-=1;
        ans-=(com(n,a)+com(n,b));
        System.out.println(ans);


    }
    static int fact(int n){
        int ans =1;
        for(int i=n;i>0;i--){
            ans*=i;
            ans=ans%MOD;
        }
        return ans;
    }

    static long com(int n,int k){
        long ans=1;
        k= Math.min(n-k,k);
        for(int i=0;i<k;i++){
            ans*=(n-i)%MOD/(i+1)%MOD;
            ans = ans%MOD;

        }
        return ans;
    }


}