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 C (Clang 3.8.0) (judge verdict: Accepted)

#include <stdbool.h>
#include <stdio.h>
#include <stdlib.h>
#include <inttypes.h>
#include <ctype.h>
#include <stdint.h>
#include <string.h>
#include <wchar.h>
#include <math.h>

#define N_MAX (100)
#define P_MAX (100)
#define DP_ARRAY_SIZE (N_MAX * P_MAX / 32 + 1)

#define MIN(a, b) ((a) < (b) ? (a) : (b))
#define MAX(a, b) ((a) > (b) ? (a) : (b))
#define ABS(a) ((a) < 0 ? -(a) : (a))
#define ABSS(a, b) ((a) > (b) ? (a) - (b) : (b) - (a))

int compare_sz_desc(const void* a, const void* b) {
    return *((size_t*)a) > * ((size_t*)b) ? -1 : 1;
}

int compare_i64_asc(const void* a, const void* b) {
    return *((int64_t*)a) < *((int64_t*)b) ? -1 : 1;
}

int compare_c_asc(const void* a, const void* b) {
    return *((char*)a) < *((char*)b) ? -1 : 1;
}

int compare_c_desc(const void* a, const void* b) {
    return *((char*)a) > * ((char*)b) ? -1 : 1;
}

int compare_f(const void* a, const void* b) {
    return *((int64_t*)a) < *((int64_t*)b) ? -1 : 1;
}

int compare_f2(const void* a, const void* b) {
    return *((uint64_t*)a) > * ((uint64_t*)b) ? -1 : 1;
}

static size_t comb(const size_t n, const size_t r) {
    size_t result = 1;

    for (size_t i = 0; i < r; i++) {
        result *= n - i;
        result /= i + 1;
    }

    return result;
}

static uint64_t combU64(const uint64_t n, const uint64_t r) {
    uint64_t result = 1;

    for (uint64_t i = 0; i < r; i++) {
        result *= n - i;
        result /= i + 1;
    }

    return result;
}

static uint64_t gcdU64(uint64_t m, uint64_t n)
{
    uint64_t temp;

    while (m % n != 0) {
        temp = n;
        n = m % n;
        m = temp;
    }

    return n;
}

static size_t gcdZu(size_t m, size_t n) {
    size_t temp;

    while (m % n != 0) {
        temp = n;
        n = m % n;
        m = temp;
    }

    return n;
}

int main(void) {
    uint64_t Q, H, S, D, N;

    scanf("%"PRIu64" %"PRIu64" %"PRIu64" %"PRIu64"\n%"PRIu64, &Q, &H, &S, &D, &N);

    uint64_t min = 4 * Q * N;

    if (2 * H * N < min) {
        min = 2 * H * N;
    }
    if (S * N < min) {
        min = S * N;
    }
    if (N / 2 * D + (N % 2) * 4 * Q < min) {
        min = N / 2 * D + (N % 2) * 4 * Q;
    }
    if (N / 2 * D + (N % 2) * 2 * H < min) {
        min = N / 2 * D + (N % 2) * 2 * H;
    }
    if (N / 2 * D + (N % 2) * S < min) {
        min = N / 2 * D + (N % 2) * S;
    }

    printf("%"PRIu64, min);

    return 0;
}