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: Time Limit Exceeded)

n, a, b = gets.split.map(&:to_i)
if n % 2 == 0
  num = n / 2 - 1
  tmp = 0
  1.upto(num) do |flower_num|
    tmp += [*n-flower_num+1..n].inject(:*) / [*1..flower_num].inject(:*)
  end
  result = 2 * tmp + 1
  plus = n / 2
  result += [*n-plus+1..n].inject(:*) / [*1..plus].inject(:*)
  result -= [*n-a+1..n].inject(:*) / [*1..a].inject(:*)
  result -= [*n-b+1..n].inject(:*) / [*1..b].inject(:*)
  puts result
else
  num = n / 2
  tmp = 0
  1.upto(num) do |flower_num|
    tmp += [*n-flower_num+1..n].inject(:*) / [*1..flower_num].inject(:*)
  end
  result = 2 * tmp + 1
  result -= [*n-a+1..n].inject(:*) / [*1..a].inject(:*)
  result -= [*n-b+1..n].inject(:*) / [*1..b].inject(:*)
  puts result
end