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 Haskell (GHC 7.10.3) (judge verdict: Wrong Answer)

m = 10^9 + 7 :: Int

modpow :: Int -> Int -> Int
modpow a n
    | n == 1 = a `mod` m
    | otherwise = (if n `mod` 2 == 1
                  then a * modpow (a `mod` m)  (n-1)
                  else modpow (a*a `mod` m) (n `div` 2)) `mod` m

fact :: Int -> Int
fact 1 = 1
fact n = n * fact (n - 1)

nCr :: Int -> Int -> Int
nCr n r = fact n * modpow (fact r) (m - 2) `mod` m

main :: IO()
main = do
  [n,a,b] <- map read . words <$> getLine
  print $ (modpow 2 n) - 1 - nCr n a - nCr n b