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: Accepted)

import kotlin.Long as Num

const val mod=1000000007

fun modpow(n:Num,p:Num=mod-2L):Num=when {
	p==0L->1L
	p%2==1L->n*modpow(n,p-1)%mod
	else-> {
		val d=modpow(n,p/2)
		d*d%mod
	}
}

fun nCr(n:Num,r:Num):Num {
	if(n-r<r)
		return nCr(n,n-r)
	var res=1L
	for(i in n-r+1..n) {
		res*=i
		res%=mod
	}
	for(i in 2..r) {
		res*=modpow(i)
		res%=mod
	}
	return res
}

fun main(args:Array<String>) {
	abc000X()
}

fun abc000X() {
	val (n,a,b)=readLine()!!.split(" ").map {it.toLong()}

	val t=modpow(2,n)
	val u=nCr(n,a)
	val v=nCr(n,b)
	println((t+mod*2-1-u-v)%mod)
}