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 int MOD = 1_000_000_007;
    public static void main(String args[]) throws Exception {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int a = sc.nextInt();
        int b = sc.nextInt();
        
        long res = ((modPow(2, n) - comb(n, a) - comb(n, b) - 1)) % MOD;
        System.out.println( res < 0 ? res + MOD : res);
    }

    private static long modPow(long a, long b) {
    	if(b == 0)
    		return 1;
    	if(a == 0)
    		return 0;
    	if(b == 1)
    		return a;
    	long res = modPow(a, b / 2) % MOD;
    	if(b % 2 == 1)
    		return ((res * res) % MOD) * a % MOD;
    	return (res * res) % MOD;
    }

    private static long factorial(long n, long start) {
    	long res = 1L;
    	for(long i = start; i <= n; i++)
    		res = (res % MOD)* (i % MOD) % MOD;
    	return res;
    }

    private static long comb(long a, long b) {
    	long factA = factorial(a, a - b + 1) % MOD;
    	long factB = factorial(b, 1) % MOD;
    	long inv = modPow(factB, MOD - 2) % MOD;
    	return factA * inv % MOD;
    }
}