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Contest: Task: Related: TaskB

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