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: Wrong Answer)

import scala.annotation.tailrec

object Main {
  val MOD = BigInt(1000000007)

  def main(args: Array[String]): Unit = {
    val sc = new java.util.Scanner(System.in)
    val total = sc.nextInt()
    val a = sc.nextInt()
    val b = sc.nextInt()

    val c_total_a = (permutation(total, a) / permutation(a, 1))
    val c_total_b = (permutation(total, b) / permutation(b, 1))
    val excepts = c_total_a + c_total_b

    val ans_total = BigInt(2).<<(total) - excepts - 1
    val ans = ans_total % MOD

    println(ans)
  }

  @tailrec
  def permutation(n: Int, k: Int, memo: BigInt = 1): BigInt = {
    if (n == k) {
      memo
    } else {
      permutation(n - 1, k, memo * n)
    }
  }
}