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)

def extended_gcd(a, b)
  last_remainder, remainder = a.abs, b.abs
  x, last_x, y, last_y = 0, 1, 1, 0
  while remainder != 0
    last_remainder, (quotient, remainder) = remainder, last_remainder.divmod(remainder)
    x, last_x = last_x - quotient*x, x
    y, last_y = last_y - quotient*y, y
  end

  return last_remainder, last_x * (a < 0 ? -1 : 1)
end

def modinv(e, et)
  g, x = extended_gcd(e, et)
  if g != 1
    raise 'The maths are broken!'
  end
  x % et
end

require 'set'; require 'prime'
INF=Float::INFINITY; MOD=10**9+7
n,a,b = gets.chomp.split.map(&:to_i)
require 'openssl'

def all(n)
  ret = 2.to_bn.mod_exp(n, MOD) - 1
  ret
end

def nck(n,k)
  ans = 1
  k.times do |i|
    ans = ans * (n-i) % MOD
    ans = ans * modinv(i+1, MOD) % MOD
  end
  ans
end

aa = nck(n,a)
bb = nck(n,b)
bb = 0 if a==b
ans = all(n) - aa - bb
while ans < 0
  ans += MOD
end
puts (ans + MOD)%MOD