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 Kotlin (1.0.0) (judge verdict: Runtime Error)

import java.util.*

fun main(args: Array<String>) {
  val (n, a, b) = readLine()!!.split(" ").map(String::toInt)
  var pattern = 0 
  (1..n).forEach {
    if(it != 1 && it != b) {
      pattern += NCR.ncr(n, it)
    }
  }
  println(pattern%(Math.pow(10.0, 9.0).toInt() + 7))
}

object NCR {
fun ncr(n: Int, r: Int): Int = kaijyou(n)/(kaijyou((n-r))*kaijyou(r))

fun kaijyou(n: Int) : Int {
  if(n == 0) return 1
  return _kaijyou(n, 1)
}

fun _kaijyou(n: Int, aac: Int): Int {
  if(n == 1) return aac
  return _kaijyou(n-1, n*aac)
}
}