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=10**9+7

def repeat_squaring n,p,m
    if p==0
        return 1
    elsif p%2==0
        t=repeat_squaring(n,p/2,m)
        return t**2%m
    end
    return n*repeat_squaring(n,p-1,m)
end

def frac n,k
  a=1
  b=1
  k.times do |i|
    b*=i+1
    b%=MOD
  end
  k.times do |i|
    j=i+1
    a*=n-i
    a%=MOD
  end
  a*inv(b)%MOD
end

def inv(n)
  repeat_squaring(n,MOD-2,MOD)
end


n,a,b=gets.split.map(&:to_i)
ans=repeat_squaring(2,n,MOD)
ans-=1

ca=MOD-frac(n,a)
cb=MOD-frac(n,b)

p (ans+ca+cb)%MOD