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)

N, A, B = gets.split.map &:to_i
MOD = 10**9+7

class Integer
  def pow(y, m)
    return 1 if y == 0
    res = self.pow(y/2, m)
    res * res % m * (y.odd? ? self : 1) % m
  end

  def comb(k, m)
    u = d = 1
    n = self
    (1..k).each{|i|
      u = u * n % m
      d = d * i % m
      n -= 1
    }
    u * d.pow(m - 2, m) % m
  end
end

p (2.pow(N, MOD) - 1 - N.comb(B, MOD) - N.comb(A, MOD)) % MOD