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 Scala (2.11.7) (judge verdict: Accepted)

object Main extends App {
	val sc = new java.util.Scanner(System.in)
	val pw = new java.io.PrintWriter(System.out)
	
	val n, a, b = sc.nextInt
	
	val M = BigInt(1000000007)
	
	def cmb(k: Int): BigInt =
		(BigInt(1) to BigInt(k)).foldLeft(BigInt(1))((z, i) => (n - k + i) * i.modInverse(M) * z % M)
		
	def pow2(k: Int): BigInt =
		if (k == 0) 1
		else if (k % 2 == 0) {
			val r = pow2(k/2)
			r * r % M
		} else BigInt(2) * pow2(k-1) % M

	val r = (pow2(n) - BigInt(1) - cmb(a) - cmb(b)) % M
	
	pw.println(r + (if(r < 0) M else 0))
	pw.flush()
}