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)

M = 10 ** 9 + 7

def pow(a, b)
    result = 1
    while b > 0
        if b & 1 == 1
            result = result * a % M
        end
        a = a ** 2 % M
        b >>= 1
    end
    result
end

def c(n, k)
    result = 1
    ((n - k + 1) .. n).each{|i|
        result = result * i % M
    }
    fact = (1..k).inject{|r, i| r * i % M}
    pow = 1
    m = M - 2
    while m > 0
        if m & 1 == 1
            pow = pow * fact % M
        end
        fact = fact * fact % M
        m /= 2
    end
    result = result * pow % M
    result
end
n, a, b = gets.split.map{|i|i.to_i}
r = pow(2, n) - 1
warn r
r -= c(n, a)
r %= M
warn r
r -= c(n, b)
r %= M
puts r