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: Runtime Error)

//import java.io.BufferedReader;
import java.io.IOException;
//import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.List;
import java.util.Scanner;

public class Main {

	public static void main(String[] args) throws IOException {

		//		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		Scanner scan = new Scanner(System.in);

		long n, a, b;

		//花の種類
		n = scan.nextLong();

		//苦手な数
		a = scan.nextLong();
		b = scan.nextLong();

		//合計通り
		long sum = 0;

		for (long n_count = 2; n_count <= n; n_count++) {
			if (n_count == a || n_count == b) {
				continue;
			}

			long bunbo, bunshi;
			bunbo = 1;
			bunshi = 1;

			long loop_count = 0;
			while (true) {
				bunshi *= n - loop_count;
				loop_count++;

				if (n_count - 1 == loop_count)
					break;
			}

			long loop_count_bunbo = 0;
			while (true) {
				bunbo *= n_count - loop_count_bunbo;
				loop_count_bunbo++;

				if (n_count - loop_count_bunbo == 1)
					break;
			}

			sum += bunshi / bunbo;

		}

		System.out.println(sum);

	}

}