Problem:
Score : 400 points

Problem Statement

Snuke has one biscuit and zero Japanese yen (the currency) in his pocket.
He will perform the following operations exactly K times in total, in the order he likes:

Hit his pocket, which magically increases the number of biscuits by one.

Exchange A biscuits to 1 yen.

Exchange 1 yen to B biscuits.

Find the maximum possible number of biscuits in Snuke's pocket after K operations.

Constraints

1 \leq K,A,B \leq 10^9

K,A and B are integers.

Input

Input is given from Standard Input in the following format:

K A B

Output

Print the maximum possible number of biscuits in Snuke's pocket after K operations.

Sample Input 1

4 2 6

Sample Output 1

7

The number of biscuits in Snuke's pocket after K operations is maximized as follows:

Hit his pocket. Now he has 2 biscuits and 0 yen.

Exchange 2 biscuits to 1 yen. his pocket. Now he has 0 biscuits and 1 yen.

Hit his pocket. Now he has 1 biscuits and 1 yen.

Exchange 1 yen to 6 biscuits. his pocket. Now he has 7 biscuits and 0 yen.

Sample Input 2

7 3 4

Sample Output 2

8

Sample Input 3

314159265 35897932 384626433

Sample Output 3

48518828981938099

Solution in Haskell (GHC 7.10.3) (judge verdict: Accepted)

import Control.Arrow
import Control.Monad
import Data.List
import qualified Data.ByteString.Char8 as B

main :: IO ()
main = readLine >>= print . solve 

solve :: [Int] -> Int
solve [k, a, b]
    | k <= a || b - a < 3 = k + 1
    | odd d = (n + 1) * (b - a) + a
    | otherwise = n * (b - a) + a + 1
    where
        d = k - a
        n = d `div` 2

readLine :: IO [Int]
readLine = unfoldr (\s -> second (maybe B.empty snd . B.uncons) <$> B.readInt s) <$> B.getLine

readContents :: Int -> IO [[Int]]
readContents = flip replicateM readLine