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.util.Scanner;

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

		int score = 0;
		int kimari = (int) (Math.pow(10, 9) + 7);

		score += (int) Math.pow(2, n);
		int minus1 = calcNumOfCombination(n, a);
		int minus2 = calcNumOfCombination(n, b);
		//		for (int i = 1; i <= n; i++) {
		//			if (i == a || i == b) {
		//				continue;
		//			}
		//			score += calcNumOfCombination(n, i);
		//		}

		System.out.println((score - minus1 - minus2 - 1) % kimari);

	}

	//組み合わせの数nCrを計算
	static int calcNumOfCombination(int n, int r) {
		int num = 1;
		for (int i = 1; i <= r; i++) {
			num = num * (n - i + 1) / i;
		}
		return num;
	}
}