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)

def power2(base, exp, mod)
  if(exp == 1)
    return base % mod;
  else
    if exp % 2 == 0
      return (power2(base, exp/2, mod) ** 2) % mod
    else
      return (base * (power2(base, (exp-1)/2, mod) ** 2)) % mod
    end
  end
end

def comb(n, k, mod)
  c = 1
  d = 1
  for i in (1..k)
    c = (c * (n - k + i)) % mod
    d = d * i
  end

  return (c * power2(d, mod - 2, mod)) % mod
end

n, a, b = gets.split.map(&:to_i)

mod = 10 ** 9 + 7

if a != b
  X = comb(n, a, mod) + comb(n, b, mod)
else
  X = comb(n, a, mod)
end
A = power2(2, n, mod) - 1 + mod
puts (A - X % mod) % mod