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 (1.3.71) (judge verdict: Wrong Answer)

fun readString() = readLine()!!
fun readInt() = readLine()!!.toInt()
fun readLong() = readLine()!!.toLong()
fun readIntList() = readLine()!!.split(" ").map(String::toInt)
fun readLongList() = readLine()!!.split(" ").map(String::toLong)
fun <T> Array<Array<T>>.print() {
    this.forEach {
        println(it.joinToString(" "))
    }
}

fun powerMod(x: Int, n: Int, mod: Int): Int = when {
    n == 2 -> ((x.toLong() * x.toLong()) % mod).toInt()
    n % 2 == 1 -> ((powerMod(x, n - 1, mod).toLong() * x.toLong()) % mod).toInt()
    else -> {
        val tmp = (powerMod(x, n / 2, mod) % mod).toLong()
        ((tmp * tmp) % mod).toInt()
    }
}

class Combination2 {
    companion object {
        fun calc(a: Int, b: Int, mod: Int): Int {
            if (b > a - b) return calc(a, a - b, mod)

            var mul = 1L
            var div = 1L

            for (i in 0 until b) {
                mul *= (a - i)
                mul %= mod
                div *= (i + 1)
                div %= mod
            }

            return ((mul * powerMod(div.toInt(), mod - 2, mod)) % mod).toInt()
        }
    }
}

const val mod = 1_000_000_007

fun main() {
    val (n, a, b) = readIntList()
    
    var numAll = powerMod(2, n, mod) - 1
    if (numAll < 0) numAll += mod
    val numA = Combination2.calc(n, a, mod)
    val numB = Combination2.calc(n, b, mod)
    var res = numAll - numA - numB
    if (res < 0) res += mod

    println(res)
}