Problem:
Score : 300 points

Problem Statement

You've come to your favorite store Infinitesco to buy some ice tea.

The store sells ice tea in bottles of different volumes at different costs.
Specifically, a 0.25-liter bottle costs Q yen, a 0.5-liter bottle costs H yen, a 1-liter bottle costs S yen, and a 2-liter bottle costs D yen.
The store has an infinite supply of bottles of each type.

You want to buy exactly N liters of ice tea. How many yen do you have to spend?

Constraints

1 \leq Q, H, S, D \leq 10^8

1 \leq N \leq 10^9

All input values are integers.

Input

Input is given from Standard Input in the following format:

Q H S D
N

Output

Print the smallest number of yen you have to spend to buy exactly N liters of ice tea.

Sample Input 1

20 30 70 90
3

Sample Output 1

150

Buy one 2-liter bottle and two 0.5-liter bottles. You'll get 3 liters for 90 + 30 + 30 = 150 yen.

Sample Input 2

10000 1000 100 10
1

Sample Output 2

100

Even though a 2-liter bottle costs just 10 yen, you need only 1 liter.
Thus, you have to buy a 1-liter bottle for 100 yen.

Sample Input 3

10 100 1000 10000
1

Sample Output 3

40

Now it's better to buy four 0.25-liter bottles for 10 + 10 + 10 + 10 = 40 yen.

Sample Input 4

12345678 87654321 12345678 87654321
123456789

Sample Output 4

1524157763907942

Solution in Haskell (GHC 7.10.3) (judge verdict: Time Limit Exceeded)

{-# LANGUAGE BangPatterns #-}
import Control.Applicative((<$>))
import Control.Monad
import Data.Map ((!))
import qualified Data.Map as M
import qualified Data.List as L
import Data.Maybe (catMaybes)
-- import qualified Data.Char as C
-- import qualified Data.IntSet as I
import Debug.Trace
--------------------------------------------
readInt    = read :: String -> Int
getInt     = readInt <$> getLine
getIntList = map readInt . words <$> getLine
int2bin 0 =  []
int2bin n =  n `mod` 2 : int2bin (n `div` 2)
----------------------------------------------

-- dp[n] = min(a[0.25]+dp[n-0.25], a[0.5]+dp[n-0.5], a[1]+dp[n-1], a[2]+dp[n-2])

main :: IO ()
main = do
  [q,h,s,d] <- map read . words <$> getLine
  n <- read <$> getLine
  let pay = M.fromList [(0.25,q),(0.5,h),(1.0,s),(2.0,d)] :: M.Map Float Integer
  print $ solve 0.5 n pay (M.fromList [(0,0),(0.25,q)])

solve :: Float -> Float -> M.Map Float Integer -> M.Map Float Integer -> Integer
solve cur n pay dp
  | cur == n+0.25  = dp!n
  | otherwise =
    let a = Just $ pay!0.25 + dp!(cur-0.25)
        b = Just $ pay!0.5  + dp!(cur-0.5)
        c = if cur >= 1 then Just ((pay!1) + (dp!(cur-1))) else Nothing
        d = if cur >= 2 then Just ((pay!2) + (dp!(cur-2))) else Nothing
    in solve (cur+0.25) n pay $ M.insert cur (minimum (catMaybes [a,b,c,d])) dp