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: Accepted)

import Control.Applicative( (<$>))

main = do
    [q_, h_, s_, d_] <- map read . words <$> getLine
    n_	<- readLn::IO Integer
    let
	min'::Integer->Integer
	min' 0 = 0
	min' 1 = q_
	min' 2 = min (2*min' 1) h_
	min' 3 = minimum [  min' 2 + min' 1 ]
	min' 4 = minimum [  min' 3 + min' 1 ,
			    2*min' 2	    ,
			    s_		    ]
	min' 5 = minimum [  min' 4 + min' 1	, 
			    min' 3 + min' 2	]
	min' 6 = minimum [  min' 5 + min' 1	    ,
			    min' 4 + min' 2	    ,
			    2*min' 3		    ]
	min' 7 = minimum [  min' 6 + min' 1,
			    min' 5 + min' 2,
			    min' 4 + min' 3]
	min' 8 = minimum [  d_,
			    min' 7 + min' 1 ,
			    min' 6 + min' 2 ,
			    min' 5 + min' 3 ,
			    2*min' 4	    ]
	units = 4*n_
	(d,m) = units `quotRem` 8
    print $ d*(min' 8) + min' m