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)


MOD = 1000000007

class Integer
  def factorial
    # 階乗 n!
    return 1 if self == 0
    (1..self).inject{|result,item|result * item % MOD}
  end

  def permutation(r)
    # 順列 nPr
    return 1 if self == 0
    s = self - r + 1
    (s..self).inject{|result,item|result * item % MOD}
  end

  def combination(r)
    r = [r, self - r].min
    return self if r == 1
    return 1 if r == 0
    self.permutation(r) * (r.factorial.inverse) % MOD
  end

  # aのn乗
  def power(n)
    res = 1
    a = self
    while (n > 0)
      if n.odd?
        res = (res * a) % MOD
      end
      a = a * a % MOD
      n >>= 1 # n / 2
    end
    return res
  end

  def inverse
    # 逆元 a^{-1} mod を計算する
    return self.power(MOD-2)
  end
end


str = gets
nab = str.chomp.split(" ").map(&:to_i)
n = nab[0]
a = nab[1]
b = nab[2]

# 0本のときは花束にならないので-1
all = 2.power(n) - 1
rem1 = n.combination(a)
rem2 = n.combination(b)
total = (all - rem1 - rem2) % MOD
p total