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 Ruby (2.3.3) (judge verdict: Wrong Answer)

Q, H, S, D = gets.chomp.split(' ').map(&:to_i)
N = gets.chomp.to_i

s = {}
s[0.25] = [Q, Q]
s[0.5] = [H, H / 2.0]
s[1] = [S, S / 4.0]
s[2] = [D, D / 8.0]

p s
s = s.sort {|(k1, v1), (k2, v2)| v1[1] <=> v2[1] }
p s

a = 0
top = s.shift
if top[0] == 2
  a += (N / top[0]) * top[1][0]
  ne = s.shift
  a += ((N % top[0]) / ne[0]) * ne[1][0]
else
  ne = s.shift
  a = (N / ne[0]) * ne[1][0]
end

p a.to_i