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: Accepted)

import java.util.*;

public class Main{
    
    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 a = Integer.parseInt(sc.next());
        int b = Integer.parseInt(sc.next());
        
        long sum = mod_pow(2, n, MOD);
        sum = (sum + MOD - 1)%MOD;
        
        long am = 1;
        long bm = 1;
        for(int i=1; i<=a; i++){
            am *= n-i+1;
            am %= MOD;
            am *= mod_pow(i, MOD-2, MOD);
            am %= MOD;
        }
        for(int i=1; i<=b; i++){
            bm *= n-i+1;
            bm %= MOD;
            bm *= mod_pow(i, MOD-2, MOD);
            bm %= MOD;
        }
        
        sum = ((sum+MOD-am)%MOD+MOD-bm)%MOD;
        
        System.out.println(sum);
    }
    
    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;
    }
}