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: Accepted)

import qualified Data.ByteString.Char8 as C
import Data.List

mdl :: Num a => a
mdl = 10^9 + 7

t a b = a * b `mod` mdl

positivize x = if x < 0 then x + mdl else x

main :: IO ()
main = do
    [n,a,b] <- unfoldr (C.readInt . C.dropWhile (==' ')) <$> C.getLine
    print $ positivize $ (powMod 2 n - 1 - chooseOpt n a - chooseOpt n b) `mod` mdl

powMod :: Int -> Int -> Int
powMod cur 0 = 1
powMod cur n
    | even n = powMod (t cur cur) (div n 2)
    | odd n  = (t cur) $! powMod (t cur cur) (div n 2)

chooseOpt n i = choose n (min (n-i) i)
    where
    choose n i = t (prod' [n-i+1..n] ) $ (prod' [1..i]) `powMod` (mdl-2)
    prod' = foldr t 1