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)

MOD = 10 ** 9 + 7

def pow(a, b)
  if b == 0
    1
  elsif b % 2 == 1
    a * pow(a, b - 1) % MOD
  else
    pow(a ** 2 % MOD, b / 2)
  end
end

def inv(n)
  pow(n, MOD - 2) % MOD
end

def comb(n, k)
  a = 1
  b = 1
  k.times do |i|
    b *= i + 1
    b %= MOD
  end
  k.times do |i|
    a *= n - i
    a %= MOD
  end
  a * inv(b) % MOD
end

N, a, B = gets.split.map(&:to_i)
ans = pow(2, N) - 1
ans += MOD - comb(N, a)
ans += MOD - comb(N, B)
puts ans % MOD