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 Common Lisp (SBCL 1.1.14) (judge verdict: Accepted)

(declaim (optimize (speed 3) (debug 0) (safety 0)))

(let ((q (read))
      (h (read))
      (s (read))
      (d (read))
      (n (read))
      (p 0))
  (setf s (min (* 4 q) (* 2 h) s))
  (when (= (mod n 2) 1)
    (setf n (- n 1))
    (setf p 1))
  (if (< (+ (* d (/ n 2)) (* p s)) (* (+ p n) s))
    (setf a (+ (* d (/ n 2)) (* p s)))
    (setf a (* (+ p n) s)))
  (format t "~A~%" a))