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.Scanner;

public class Main {
    static long mod = 1000000007;
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        long n = sc.nextLong(), a = sc.nextLong(), b = sc.nextLong();
        long ans = pow(2, n) - comb(n, a) - comb(n, b) - 1;
        if(ans < 0) ans += (-ans / mod + 1) * mod;
        System.out.println(ans);
    }
    static long pow(long x, long n) {
        long a = 1;
        do {
            if((n & 1) == 1) a = (a * x) % mod;
            x = (x * x) % mod;
        } while((n >>= 1) > 0);
        return a;
    }
    static long comb(long n, long r) {
        long mol = n, den = r;
        for(int i = 1; i < r; i++) {
            mol = (mol * (n - i)) % mod;
            den = (den * i) % mod;
        }
        return mol * pow(den, mod - 2) % mod;
    }
}