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)

const val MOD = 1000000007L
fun main(args: Array<String>) {
    val (N, A, B) = listOfInt()
    fun pow2(n: Int): ModInt {
        if (n == 0) return ModInt(1)
        var x = pow2(n / 2)
        x *= x
        if (n % 2 == 1) x *= 2
        return x
    }
    fun C(n: Int, a: Int): ModInt {
        var x = ModInt(1)
        var y = ModInt(1)
        repeat(a) { i ->
            x *= n - i
            y *= i + 1
        }
        return x / y
    }
    var ans = pow2(N)
    ans -= 1
    ans -= C(N, A)
    ans -= C(N, B)
    println(ans.toString())
}
fun next() = readLine()!!
fun nextInt() = Integer.parseInt(next())
fun listOfString() = next().split(" ")
fun listOfInt() = listOfString().map(String::toInt)


data class ModInt(private var v: Long) {
    companion object {
        private const val MOD = 1000000007L
    }
    init {
        if (v >= MOD) v %= MOD
    }
    constructor(n: Int): this(n.toLong())
    operator fun plus(other: Int): ModInt {
        val x = v + other
        if (x >= MOD) {
            return ModInt(x - MOD)
        }
        return ModInt(x)
    }
    operator fun minus(other: Int): ModInt {
        val x = v + MOD - other
        if (x >= MOD) {
            return ModInt(x - MOD)
        }
        return ModInt(x)
    }
    operator fun minus(other: ModInt): ModInt {
        val x = v + MOD - other.v
        if (x >= MOD) {
            return ModInt(x - MOD)
        }
        return ModInt(x)
    }
    operator fun times(other: Int): ModInt {
        return ModInt(v * other % MOD)
    }
    operator fun times(other: ModInt): ModInt {
        return ModInt(v * other.v % MOD)
    }
    operator fun div(other: ModInt): ModInt {
        return ModInt(v * calc(other.v, MOD - 2) % MOD)
    }
    private fun calc(a: Long, b: Long): Long {
        if (b == 0L) return 1L
        if (b % 2L == 0L) {
            val d = calc(a, b / 2)
            return d * d % MOD
        }
        return a * calc(a, b - 1) % MOD
    }
    override fun toString(): String {
        return v.toString()
    }
}