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)

item = gets.chomp.split(/\s+/).map { |e| e.to_i }
n = item[0]
a = item[1]
b = item[2]

def modpow(a, b, mod)
  res = 1
  while (b > 0)
    if (b % 2 == 1)
      res = res * a % mod
    end
    a = a * a % mod
    b >>= 1
  end
  res
end

sum = modpow(2, n, 10**9+7) - 1

def combi(n,k)
  k=n-k if 2*k > n
  return 1 if k == 0
  ((n-k+1)..n).reduce(&:*)/((1..k).reduce(&:*))
end

sum -= combi(n, a) % (10**9+7)
sum -= combi(n, b) % (10**9+7)

if sum < 0
  sum += 10**9 + 7
end

puts sum