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 Control.Monad
import Data.Maybe
import qualified Data.ByteString.Char8 as BS

main :: IO()
main = do
    [n,a,b] <- getIntList
    -- ΣnCk[0,n] = 2^n より (2^n - 1 - nCa - nCb)が答
    putStrLn $ show $ let result = (power' 2 n) - 1 - (combination n a) - (combination n b)
                          divisor = 10^9 + 7
                      in snd $ divMod (result + 2 * divisor) divisor

fact' :: (Integral a) => a -> a -> a
fact' a 1 = a
fact' a n
    | a < n  = -1
    | a >= n = snd $ (a * fact' (a-1) (n-1)) `divMod` p
    where p = 10^9 + 7

power' :: (Integral a) => a -> a -> a
power' 1 _ = 1
power' a 1 = a
power' a b = let ret = snd $ divMod (x * x) p
             in if even b then ret else snd $ divMod (ret * a) p
             where p = 10^9 + 7
                   x = power' a $ fst (b `divMod` 2)

inv :: (Integral a) => a -> a -> a
inv n p = if n <= 0 || p <= 1
              then -1
              else power' n (p-2)

combination :: (Integral a) => a -> a -> a
combination 0 _ = 1
combination _ 0 = 1
combination m 1 = m
combination m n
    | m < n  = 0
    | m == n = 1
    | n > threshold  = combination m (m-n)
    | n <= threshold = snd $ ((fact' m n) * (inv (fact' n n) divisor)) `divMod` divisor
    where threshold = fst $ divMod m 2
          divisor = 10^9 + 7

readInt = fst . fromJust . BS.readInteger
readIntList = map readInt . BS.words
getIntList = readIntList <$> BS.getLine