Problem:
Score : 400 points

Problem Statement

You start with the number 0 and you want to reach the number N.

You can change the number, paying a certain amount of coins, with the following operations:

Multiply the number by 2, paying A coins.

Multiply the number by 3, paying B coins.

Multiply the number by 5, paying C coins.

Increase or decrease the number by 1, paying D coins.

You can perform these operations in arbitrary order and an arbitrary number of times.

What is the minimum number of coins you need to reach N?

You have to solve T testcases.

Constraints

1 \le T \le 10

1 \le N \le 10^{18}

1 \le A, B, C, D \le 10^9

All numbers N, A, B, C, D are integers.

Input

The input is given from Standard Input. The first line of the input is

T

Then, T lines follow describing the T testcases.
Each of the T lines has the format

N A B C D

Output

For each testcase, print the answer on Standard Output followed by a newline.

Sample Input 1

5
11 1 2 4 8
11 1 2 2 8
32 10 8 5 4
29384293847243 454353412 332423423 934923490 1
900000000000000000 332423423 454353412 934923490 987654321

Sample Output 1

20
19
26
3821859835
23441258666

For the first testcase, a sequence of moves that achieves the minimum cost of 20 is:

Initially x = 0.

Pay 8 to increase by 1 (x = 1).

Pay 1 to multiply by 2 (x = 2).

Pay 1 to multiply by 2 (x = 4).

Pay 2 to multiply by 3 (x = 12).

Pay 8 to decrease by 1 (x = 11).

For the second testcase, a sequence of moves that achieves the minimum cost of 19 is:

Initially x = 0.

Pay 8 to increase by 1 (x = 1).

Pay 1 to multiply by 2 (x = 2).

Pay 2 to multiply by 5 (x = 10).

Pay 8 to increase by 1 (x = 11).

Solution in Java (OpenJDK 11.0.6) (judge verdict: Accepted)



import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.Arrays;
import java.util.Comparator;
import java.util.HashSet;
import java.util.PriorityQueue;
import java.util.Scanner;
import java.util.Set;

public final class Main {

    public static void main(String[] args) {
        final Scanner in = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
        final int t = in.nextInt();
        for (int i = 0; i < t; i++) {
            final long n = in.nextLong();
            final int a = in.nextInt();
            final int b = in.nextInt();
            final int c = in.nextInt();
            final int d = in.nextInt();
            in.nextLine();
            System.out.println(dfs(n, a, b, c, d));
        }
    }

    private static long dfs(long n, int a, int b, int c, int d) {
        final Set<Long> seen = new HashSet<>();
        final PriorityQueue<long[]> q = new PriorityQueue<>(Comparator.comparingLong(l -> l[1]));
        q.offer(new long[] { n, 0 });
        while (!q.isEmpty()) {
            final long[] curr = q.remove();
//            System.out.println(Arrays.toString(curr));
            if (curr[0] == 0) {
                return curr[1];
            }
            if (!seen.add(curr[0])) {
                continue;
            }
            q.offer(new long[] { curr[0] / 5, curr[1] + c + (d * (curr[0] % 5)) });
            q.offer(new long[] { (curr[0] / 5) + 1, curr[1] + c + (d * (5 - (curr[0] % 5))) });
            q.offer(new long[] { curr[0] / 3, curr[1] + b + (d * (curr[0] % 3)) });
            q.offer(new long[] { (curr[0] / 3) + 1, curr[1] + b + (d * (3 - (curr[0] % 3))) });
            q.offer(new long[] { curr[0] / 2, curr[1] + a + (d * (curr[0] % 2)) });
            q.offer(new long[] { (curr[0] / 2) + 1, curr[1] + a + (d * (2 - (curr[0] % 2))) });
            if (curr[0] <= Math.floorDiv(Long.MAX_VALUE, d) && curr[1] + curr[0] * d > 0) {
                q.offer(new long[] { 0, curr[1] + curr[0] * d });
            }
        }
        return -1;
    }
}