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.split.map(&:to_i)
n = gets.to_i

ans = 0
now = 0

a = []
a.push({b: q, l: q*8, n: 0.25})
a.push({b: h, l: h*4, n: 0.5})
a.push({b: s, l: s*2, n: 1})
a.push({b: d, l: d, n: 2})
a.sort!{ |x, y| x[:l] <=> y[:l] }

a.each do |aa|
  nn = (n - now) / aa[:n]
  next if nn < 1
  now += aa[:n] * nn
  ans += aa[:b] * nn
  break if now.to_i == n.to_i
end
puts ans.to_i