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 Ruby (2.3.3) (judge verdict: Wrong Answer)

# frozen_string_literal: true

n, a, b = gets.split.map(&:to_i)
class Integer
  def factorial
    return 1 if self == 0
    (1..self).inject(:*)
  end

  def permutation(r)
    return 1 if self == 0
    s = self - r + 1
    (s..self).inject(:*)
  end

  def combination(r)
    r = [r, self - r].min
    return self if r == 1
    return 1 if r == 0
    self.permutation(r) / r.factorial
  end
end

result = 0
(0...(n / 2)).to_a.each do |f|
  result += n.combination(f)
end

result *= 2

if n.even?
  result += n.combination((n / 2))
end
result = result - n.combination(a) - n.combination(b) - 1
puts result % (1000000000 + 7)