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 choose(n, r, mod = 10 ** 9 + 7)
  fact2(n - r + 1, n, mod) \
    * modpow(fact2(1, r, mod), mod - 2, mod) \
    % mod
end

# 分割統治法を使用
def fact2(l, r, mod = 10 ** 9 + 7)
  return 1 if l == 0 || r == 0
  return r if l == r
  return l * r % mod if r - l == 1
  half = (l + r) / 2
  (fact2(l, half, mod) % mod) \
    * (fact2(half + 1, r, mod) \
    % mod) \
    % mod
end

def modpow(n, p, mod = 10 ** 9 + 7)
  res = 1
  while p > 0
    if p & 1 == 1
      res = (res * n) % mod
    end
    n = (n ** 2) % mod
    p >>= 1
  end
  res
end
# require 'pry'
MOD = 10 ** 9 + 7
N, A, B = gets.split.map(&:to_i)
# binding.pry
puts (((modpow(2, N, MOD) + (MOD - 1)) \
  % MOD \
  + (MOD - choose(N, A, MOD))) \
  % MOD \
  + (MOD - choose(N, B, MOD))) \
  % MOD