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)

fun main(args: Array<String>) {
    val mod = 1000000007L
    fun pow(a: Long, b: Long): Long {
        var bt = b
        var ret: Long = 1
        var tmp = a
        while (bt > 0) {
            if (bt and 1 == 1L) ret = ret * tmp % mod
            tmp = tmp * tmp % mod
            bt = bt shr 1
        }
        return ret
    }

    fun nCk(n: Long, k: Long): Long {
        var ret: Long = 1
        val min = Math.min(k, n - k)
        for (i in 1..min) {
            ret = ret * pow(i, (mod - 2)) % mod
        }
        for (i in n - min + 1..n) {
            ret = ret * i % mod
        }
        return ret
    }
    val (n, a, b) = readLine()!!.split(' ').map(String::toLong)
    var base = pow(2, n) - 1 + mod
    val minus = (nCk(n, a) + nCk(n, b))%mod
    println((base - minus) % mod)
}