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)

MOD = 10 ** 9 + 7

class ModCombination
  attr_reader :fac, :inv, :finv, :mod

  MOD = 10 ** 9 + 7

  def initialize(n, mod: MOD)
    @mod = mod
    @finv = [1.mod_inverse, 1.mod_inverse]

    (2..n).each do |i|
      @finv[i] = finv[i - 1] * i.mod_inverse % mod
    end
  end

  def combination(n, k)
    return 0 if n < k
    return 0 if n < 0 || k < 0

    fa = 1

    n.downto(n - k + 1) do |i|
      fa = (fa * i) % mod
    end

    (fa * finv[k]) % mod
  end
end

class Integer
  def mod_pow(n, mod = MOD)
    x = self
    res = 1

    while n > 0
      res = res * x % mod if n[0] == 1
      x = x * x % mod
      n >>= 1
    end

    res
  end

  def mod_inverse(mod = MOD)
    mod_pow(mod - 2, mod)
  end
end

N, A, B = gets.split.map(&:to_i)
mc = ModCombination.new([A, B].max)

puts (2.mod_pow(N) - mc.combination(N, A) - mc.combination(N, B) - 1) % MOD