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: Runtime Error)

// import kotlin.comparisons.*
// import kotlin.math.*
import java.util.*

const val mod = 1000000007L

fun readI() = readLine()!!.toInt()
fun readL() = readLine()!!.toLong()
fun readD() = readLine()!!.toDouble()
fun readIs() = readLine()!!.split(' ').map(String::toInt)
fun readLs() = readLine()!!.split(' ').map(String::toLong)
fun readDs() = readLine()!!.split(' ').map(String::toDouble)

fun repeatpow(base: Long, exp: Long): Long {
  if (exp == 0L) return 1
  if (exp % 2 == 0L) {
    val w = repeatpow(base, exp / 2)
    return w * w % mod
  } else {
    val w = repeatpow(base, exp - 1)
    return base * w % mod
  }
}

fun main(args: Array<String>) {
  val (n, a, b) = readIs()
  val fa = (1L..a).reduce { a1, a2 -> a1 * a2 % mod }
  val fb = fa * ((a + 1L)..b).reduce { a1, a2 -> a1 * a2 % mod } % mod
  var w1 = 1L
  val w2 = LongArray(b) { w1 = w1 * (n - it) % mod; w1 }
  val na = w2[a - 1]
  val nb = w2[b - 1]

  val ans = repeatpow(2, n.toLong()) -
    na * repeatpow(fa, mod - 2) % mod -
    nb * repeatpow(fb, mod - 2) % mod -
    1
    println(if (ans < 0) ans + mod else ans)
}