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 JavaScript (node.js v5.12) (judge verdict: Time Limit Exceeded)

function parseInput(input) {
  const values = []
  input.split('\n').forEach(row => {
    const list = row.split(' ')
    list.forEach(v => values.push(v))
  })

  return values
}

function getInput() {
  const dummy = `1000000000 141421 173205`
  return parseInput(dummy || require('fs').readFileSync('/dev/stdin', 'utf8'))
}

function factorial(num) {
  var number = 1
  for (var i = 1; i <= num; i++) {
    console.log(number);
    number *= i
  }
  return number
}

function combination(n, r) {
  return factorial(n) / (factorial(r) * factorial(n - r))
}

;(function main() {
  const input = getInput()
  const n = +input[0]
  const a = +input[1]
  const b = +input[2]

  var sum = 0
  for (var r = 1; r <= n; r++) {
    if (r === a || r === b) {
      continue
    }

    sum += combination(n, r)
  }

  const c = Math.pow(10, 9) + 7
  console.log(sum % c)
})()