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)

n, a, b = gets.split.map(&:to_i)
MOD = 10 ** 9 + 7

def power(x, n)
    return 1 if n == 0
    (n.even? ? 1 : x) * power(x ** 2 % MOD, n / 2) % MOD
end

def mul(s, t)
    (s..t).each.inject(1) {|r, v| r * v % MOD}
end

def comb(a, b)
    mul(a - b + 1, a) * power(mul(1, b), MOD - 2) % MOD 
end

puts (power(2, n) - 1 - comb(n, a) - comb(n, b)) % MOD