Problem:
Score : 200 points

Problem Statement

Square1001 has seen an electric bulletin board displaying the integer 1.
He can perform the following operations A and B to change this value:

Operation A: The displayed value is doubled.

Operation B: The displayed value increases by K.

Square1001 needs to perform these operations N times in total.
Find the minimum possible value displayed in the board after N operations.

Constraints

1 \leq N, K \leq 10

All input values are integers.

Input

Input is given from Standard Input in the following format:

N
K

Output

Print the minimum possible value displayed in the board after N operations.

Sample Input 1

4
3

Sample Output 1

10

The value will be minimized when the operations are performed in the following order: A, A, B, B.

In this case, the value will change as follows: 1 → 2 → 4 → 7 → 10.

Sample Input 2

10
10

Sample Output 2

76

The value will be minimized when the operations are performed in the following order: A, A, A, A, B, B, B, B, B, B.

In this case, the value will change as follows: 1 → 2 → 4 → 8 → 16 → 26 → 36 → 46 → 56 → 66 → 76.

By the way, this contest is AtCoder Beginner Contest 076.

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

import Data.List(minimum)
opA :: Int -> Int
opA i = 2 * i


opB :: Int -> Int -> Int
opB i k = i + k

choose :: Int -> Int -> Int
choose i k = minimum [reA, reB]
  where
    reA = opA i
    reB = opB i k

likeFor :: [Int] -> Int -> [Int] -> [Int]
likeFor [] k acc = acc
likeFor src k acc = likeFor (tail src) k acc'
  where
    acc' = (choose (head acc) k) : acc

main = do
  ns <- fmap (fmap (read :: String -> Int) . words) . lines <$> getContents
  let n = head $ head ns
  let k = head $ last ns
  let result = likeFor (replicate n 0) k [1]
  putStrLn $ show $ head result