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: Runtime Error)

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)
	val fac, finv, inv = Array.fill(n)(BigInt(1))
	
    for(i <- (2 until fac.size)) {
    	val bi = BigInt(i)
    	fac(i) = fac(i - 1) * bi % M
    	inv(i) = M - inv((M % bi).toInt) * (M / bi) % M
    	finv(i) = finv(i - 1) * inv(i) % M
    }
    
    def cmb(k: Int): BigInt =
    	if (n < k) 0
    	else if (n < 0 || k < 0) 0
    	else fac(n) * (finv(k) * finv(n - k) % M) % M;

	pw.println((1 to n).filter(i => i != a && i != b).foldLeft(BigInt(0))((z, i) => (z + cmb(i)) % M).toInt)
	pw.flush()
}