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 (2.7.1) (judge verdict: Accepted)

require 'set'

class Hash
  def push(key, value)
    self[key] = [] if self[key] == nil
    self[key].push(value)
  end
end

class Array
  def lower_bound(value)
    left = -1;
    right = self.length;
    while left + 1 < right
      mid = left + (right - left) / 2;
      if self[mid] >= value
        right = mid
      else
        left = mid
      end
    end
    right
  end

  def unique
    res = [self.first]
    each_cons(2) do |a, b|
      if a != b
        res.push(b)
      end
    end
    res
  end
end

def get_ints
  gets.split.map(&:to_i)
end

def get_ints_minus_one
  get_ints.map { |x| x - 1 }
end

def get_int
  gets.chomp.to_i
end

N, A, B = get_ints

MOD= 10 ** 9  + 7

# 2 ** N - N - nCa - nCb

# mod m での aの逆元
def modinv(a, m)
  b = m; u = 1; v = 0

  while b != 0
    t = a / b
    a -= t * b
    c = a; a = b; b = c
    u -= t * v
    c = u; u = v; v = c
  end
  u %= m
  if u < 0
    u += m
  else
    u
  end
end

# nCa
ue = 1
shita = 1
A.times do |a|
  ue = ue * (N - a) % MOD
  shita = shita * (A - a) % MOD
end

nCa = ue * modinv(shita, MOD) % MOD

# nCb
ue = 1
shita = 1
B.times do |a|
  ue = ue * (N - a) % MOD
  shita = shita * (B - a) % MOD
end

nCb = ue * modinv(shita, MOD) % MOD

def exponential_with_mod(n, k, mod)
  return 1 if k == 0
  return n if k == 1

  if k % 2 == 1
    (n * (exponential_with_mod(n, k/2, mod) ** 2 % mod)) % mod
  else
    (exponential_with_mod(n, k/2, mod) ** 2) % mod
  end
end

# 2 ^ n
nn = exponential_with_mod(2, N, MOD)

ans = nn - 1 - nCa - nCb
while ans < 0
  ans += MOD
end

puts ans