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)

n,a,b = gets.chomp.split.map(&:to_i)
MOD = 10**9 + 7

def cmb(n,k)
  res = 1
  i = k
  j = 1
  while i > 0
    res = res * (n-i+1)
    res %= MOD
    j *= i
    j %= MOD
    i -= 1
  end
  res *= inv(j)
  res %= MOD
  res
end

def pow(base,exponent)
  raise ArgumentError if exponent < 0
  # 指数が0の時は結果は1です
  return 1 if exponent==0
  # 結果が出る変数を用意
  result = 1
  # 指数が1なら終了
  while exponent != 1 do
    # 指数が奇数の時、その時の底はここでresultに掛けてしまい、指数を一つ減らす
    if exponent.odd? then
      result *= base
      exponent -= 1
    end
    # 指数を2で割る
    exponent /= 2
    # 底の2乗を新たな底とする
    base *= base
    base = base % MOD
    # 繰り返す
  end
  result *= base
  # 結果を返す
  return result
end

def inv(x)
  res = 1 # 逆元をどんどんかけるやつ
  beki = x # 逆元を計算したい値のMOD化でのべき乗
  (MOD - 2).to_s(2).reverse.chars do |digest|
    res = (beki * res) % MOD if digest == '1'
    beki = (beki * beki) % MOD
  end
  res
end

if a == b
  p (pow(2, n) - cmb(n, a) - 1) % MOD
else
  p (pow(2, n) - cmb(n, a) - cmb(n, b) - 1) % MOD
end