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 {

	public static long MOD = 1_000_000_007;

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		long n = sc.nextLong();
		long a = sc.nextLong();
		long b = sc.nextLong();
		
		long aa = 1;
		long bb = 1;
		for (int i=0;i<a;i++) {
			aa=div(aa*(n-i)%MOD, i+1)%MOD;
		}
		for (int i=0;i<b;i++) {
			bb=div(bb*(n-i)%MOD, i+1)%MOD;
		}
		 System.out.println((power(2, n)-aa-bb-1+MOD*3)%MOD);



	
	}
	
	static long power (long x, long y) {
		if (y==0) {
			return 1;
		} else if (y%2==0) {
			long a = power(x, y/2);
			return a*a%MOD;
		} else {
			long a = power(x,y/2);
			return a*a%MOD*x%MOD;
		}
	}
	
	static long div (long x, long y) {
		return (x * power(y,MOD-2))%MOD;
	}
	

}