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: Time Limit Exceeded)

import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int kindsOfFlowers = scanner.nextInt();
        int a = scanner.nextInt();
        int b = scanner.nextInt();

        long answer = 0;
        if (a != 1 && b != 1) {
            answer += kindsOfFlowers;
        }

        for (int i = 2; i <= kindsOfFlowers; i++) {
            double temp = countForOneCombination(kindsOfFlowers - i + 1);
            answer += temp;
        }
        if (a != 1) {
            answer -= countForOneCombination(kindsOfFlowers - a + 1);
        }
        if (b != 1) {
            answer -= countForOneCombination(kindsOfFlowers - b + 1);
        }
        System.out.println(answer);
    }

    private static double countForOneCombination(long i) {
        double pow = Math.pow(10.0, 9.0) + 7;
        return ((i * (i + 1)) / 2.0) % pow;
    }
}