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)

# Your code here!
M = 10**9+7
def square(n, m, a)
    return 1 if m == 0
    x = square(n, m/2, a)**2 % a
    x *= n if m % 2 == 1
    return x % a
end
def hoge(num, except)
    x, y = 1, 1
    except.times do |i|
        x *= num - i
        x %= M
        y *= i+1
        y %= M
    end
    x * square(y, M-2, M) % M
end

num, a, b= gets.chop.split.map(&:to_i)
all = square(2, num, M)
all -= 1
ca = M-hoge(num, a)
cb = M-hoge(num, b)
p (all + ca + cb) % M