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: Time Limit Exceeded)

import java.util.*

fun main(args: Array<String>) {
    val sc = Scanner(System.`in`)
    val n = sc.nextLong()
    val a = sc.nextLong()
    val b = sc.nextLong()
    println(problem156d(n, a, b))
}

fun problem156d(n: Long, a: Long, b: Long): Long {
    val mod: Long = (Math.pow(10.0, 9.0) + 7).toLong()
    fun calcNumOfCombination(n: Long, r: Long): Long {
        var num = 1L
        for (i in 1..r) {
            num = (num * (n - i + 1L) / i) % mod
        }
        return num
    }

    fun a(num: Long, n: Long, r: Long): Long {
        val mod: Long = (Math.pow(10.0, 9.0) + 7).toLong()
        return (num * (n - r + 1L) / r) % mod
    }

    var sum = 0L
    var prev = -1L
    for (i in 1..n) {
        prev = if (prev == -1L) {
            calcNumOfCombination(n, i)
        } else {
            a(prev, n, i)
        } % mod
        if (i == a || i == b) continue
        sum += prev
    }
    return sum
}