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 (2.7.1) (judge verdict: Time Limit Exceeded)

#!/usr/bin/env ruby
n, a, b = gets.chomp.split.map(&:to_i)
p = 10 ** 9 + 7
@fact = [1, 1]
@factinv = [1, 1]
@inv = [0, 1]

def cmb(n, r, p)
 return 0 if r < 0 || n < r

 r = [r, n - r].min
 @fact[n] * @factinv[r] * @factinv[n-r] % p
end

2.upto(n + 1) do |i|
 @fact.push((@fact[-1] * i) % p)
 @inv.push((-@inv[p % i] * (p / i)) % p)
 @factinv.push((@factinv[-1] * @inv[-1]) % p)
end

puts 2 ** n - 1 - cmb(n, a, p) - cmb(n, b, p)