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

def pow(n, power, mod)
  return 1 if power == 0
  res = pow(n, power/2, mod)
  res * res % mod * (power.odd? ? n : 1) % mod
end

def comb(n, k, mod)
  x = y = 1
  (1..k).each do |i|
    x = x * n % mod
    y = y * i % mod
    n -= 1
  end
  x * pow(y, mod - 2, mod) % mod
end
 
puts (pow(2, n, mod) - 1 - comb(n, b, mod) - comb(n, a, mod)) % mod