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: Runtime Error)

factor = {}
factor[1] = 1
n, a, b = gets.split.map(&:to_i)
k = 1
for i in 2..n
  factor[i] = factor[i-1] * i
end
ans = 0
if n % 2 == 0
  while k < n / 2
    fact = (factor[n] / factor[n-k])
    fact /= factor[k]
    fact *= 2
    ans += fact
    k += 1
  end
  ans += 1
  fact = (factor[n] / factor[n / 2])
  fact /= factor[n / 2]
  ans += fact
else
  while k < n / 2
    fact = (factor[n] / factor[n-k])
    fact /= factor[k]
    fact *= 2
    ans += fact
    k += 1
  end
  ans += 1
end
a = n - a if a > n / 2
b = n - b if b > n / 2
fact = (factor[n] / factor[n - a])
fact /= factor[a]
ans -= fact
fact = (factor[n] / factor[n - b])
fact /= factor[b]
ans -= fact
puts ans % (10 ** 9 + 7)