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.io.BufferedReader;
import java.io.InputStreamReader;
import java.math.BigInteger;
import java.util.Scanner;

public class Main {

    public static final BigInteger MOD = new BigInteger("1000000007");

    public static void main(String[] args) {
        final Scanner in = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
        final int n = in.nextInt();
        final int a = in.nextInt();
        final int b = in.nextInt();
        final long all = fast_pow(2, n) - 1;
        System.out.println((all - c(n, a) - c(n, b) + 1_000_000_007) % 1_000_000_007);

    }

    private static long c(int top, int bottom) {
        long result = 1;
        bottom = Math.min(bottom, top - bottom);
        for (int i = 0; i < bottom; i++) {
            result *= top - i;
            result %= 1_000_000_007;
        }
        for (int i = 1; i <= bottom; i++) {
            final int target = new BigInteger(String.valueOf(i)).modInverse(MOD).intValue();
            result *= target;
            result %= 1_000_000_007;
        }
        return result;
    }

    private static long fast_pow(int base, int top) {
        if (top == 0) {
            return 1;
        }
        final long temp = fast_pow(base, top / 2);
        if (top % 2 == 0) {
            return ((temp % 1_000_000_007) * (temp % 1_000_000_007)) % 1_000_000_007;
        } else {
            return (base * (temp % 1_000_000_007) * (temp % 1_000_000_007)) % 1_000_000_007;
        }
    }
}