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: Accepted)

class Integer
  def inverse(m)
    return Rational(1, self) if m.nil?

    a, b, u, v = self, m, 1, 0
    until b.zero?
        a, (t, b) = b, a.divmod(b)
        u, v = v, u - t * v
    end

    u = -u if a < 0
    u % m
  end
end

require 'openssl'

n, a, b = gets.chomp.split.map(&:to_i)
mod = 10**9 + 7

k = a > b ? a : b
cb = [] * (k + 1)
cb[0] = 1
1.upto(k) do |i|
  cb[i] = cb[i - 1] * (n - i + 1) * i.inverse(mod) % mod
end

puts (2.to_bn.mod_exp(n, mod).to_i - cb[a] - cb[b] - 1) % mod