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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.Arrays;
import java.util.PriorityQueue;
import java.util.Scanner;

class Main {
	public static void main(String[] args) {
		new Main().run();
	}

	void run() {
		Scanner sc = new Scanner(System.in);
		long[] a = { sc.nextLong(), sc.nextLong(), sc.nextLong(), sc.nextLong() };
		long N = sc.nextLong();
		class State implements Comparable<State> {
			double volume;
			long value;

			public State(double volume_, long value_) {
				volume = volume_;
				value = value_;
			}

			public int compareTo(State o) {
				return Double.compare(value / volume, o.value / o.volume);
			};
		}
		PriorityQueue<State> pq = new PriorityQueue<>();
		pq.add(new State(0.25, a[0]));
		pq.add(new State(0.5, a[1]));
		pq.add(new State(1, a[2]));
		pq.add(new State(2, a[3]));
		double cost = 0;
		double cur = 0;
		while (Math.abs(N - cur) > 0.000001) {
			State s = pq.poll();
			int num = (int) ((N - cur) / s.volume);
			cost += s.value * num;
			cur += s.volume * num;
		}
		System.out.println((long) cost);
	}

	void tr(Object... objects) {
		System.out.println(Arrays.deepToString(objects));
	}
}