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: Wrong Answer)

fun modCnr(n: Long, r: Long, mod: Long): Long {
    val l: Long = n - r + 1
    var nt = 1L
    var i = 0
    while (n - i >= l) {
        nt = (nt * (n - i)) % mod
        i++
    }

    var rt = 1L
    var j = 0
    while (j < r) {
        rt = (rt * (r - j)) % mod
        j++
    }
    return (nt * modPow(rt, mod - 2, mod)) % mod
}

fun modPow(n: Long, ex: Long, mod: Long): Long {
    var x = n
    var remain = ex
    var result = 1L
    while (remain > 0) {
        if (remain % 2L == 1L) {
            result = (result * x) % mod
        }
        x = (x * x) % mod
        remain /= 2
    }
    return result
}

fun main(args: Array<String>) {
    val (n, a, b) = readLine()?.split(" ")?.map(String::toLong) ?: return
    val mod = 1000000007L

    val np = modPow(2, n, mod)
    val ncra = modCnr(n, a, mod)
    val ncrb = modCnr(n, b, mod)

    println((np - ncra - ncrb - 1 + mod) % mod)
}