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: Time Limit Exceeded)

import java.util.Scanner

object Main extends App {
  val sc = new Scanner(System.in)
  val n = sc.nextInt()
  val a = sc.nextInt()
  val b = sc.nextInt()

  val x = (1 to n).filterNot(i => i == a || i == b)

  val max = 200000
  val mod = 1000000007

  val fac = new Array[Long](max)
  val finv = new Array[Long](max)
  val inv = new Array[Long](max)

  def COMInit(): Unit = {
    fac(0) = 1
    fac(1) = 1
    finv(0) = 1
    finv(1) = 1
    inv(1) = 1
    for (i <- 2 until max) {
      fac(i) = fac(i - 1) * i % mod
      inv(i) = mod - inv(mod % i) * (mod / i) % mod
      finv(i) = finv(i - 1) * inv(i) % mod
    }
  }
  COMInit()

  def COM(n: Int, k: Int): Long = {
    if (n < k) 0L
    else if (n < 0 || k < 0) 0L
    else fac(n) * (finv(k) * finv(n - k) % mod) % mod
  }

  val y = x.map(COM(n, _)).sum

  println(y)
}