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 n,a,b = sc.nextInt
  def power(x:Int,p:Int):Int = if(p==0) 1 else x * power(x,p-1)
  def prod(x:Int):Int = if (x <= 1) 1 else x * prod(x - 1)
  def comb(n:Int,r:Int):Int= prod(n) / ( prod(n-r) * prod(r) ) 
  val array:Seq[Int] = for ( v <- 2 to n if a != v & b != v) yield comb(n,v)
  println(if (array.isEmpty) 0 else array.foldLeft(0)((a,b)=>a+b)%(power(10,9)+7))
}