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: Time Limit Exceeded)

n,a,b = gets.chomp.split(' ').map(&:to_i)
mod = 1000000007
def pow_num(num,n)
    if n == 0
        return 1
    end
    x = pow_num(num,n/2)
    x *= x
    if n%2==1
        x *= num
    end
    return x%1000000007
end

def multiple(s,num)
    big_num = 1
    num.times do
        big_num *= s
        s -=1
    end
    return big_num
end
a_x = multiple(n,a)
a_y = multiple(a,a) 
b_x = multiple(n,b)
b_y = multiple(b,b)


puts (pow_num(2,n)%mod-1-((a_x*pow_num(a_y,mod-2))%mod)-((b_x*pow_num(b_y,mod-2))%mod))%mod

# puts (pow_two(2,n)%mod-1-((a_x/a_y)%mod)-((b_x/b_y)%mod))%mod