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 C# (.NET Core 3.1.201) (judge verdict: Wrong Answer)

using System;
using System.Text;
using System.Collections.Generic;
using System.Linq;

public class HelloWorld
{

    static long A;
    static long B;
    static long C;
    static long D;
    static long N;
    static SortedDictionary<long, long> dic;
    static public void Main()
    {
        var T = long.Parse(Console.ReadLine());
        for (int i = 0; i < T; i++)
        {
            var inp =
            Console.ReadLine().Split(' ').Select(x => long.Parse(x)).ToArray();
            N = inp[0];
            //used = new long[N + 5];
            A = inp[1];
            B = inp[2];
            C = inp[3];
            D = inp[4];
            dic = new SortedDictionary<long, long>();
            dic.Add(1, D);
            dic.Add(0, 1000000000000000 );
            Console.WriteLine(Check(N));
        }
    }

    static long Check(long n)
    {

        if (dic.ContainsKey(n)) return dic[n];

        var tmp2 = n % 2;
        var tmp3 = n % 3;
        var tmp5 = n % 5;
        long ans = long.MaxValue;

        if (n % 5 == 0)
        {
            ans = Math.Min(ans, C + Check(n / 5));
        }
        else
        {
            ans = Math.Min(ans, C + D * (5 - tmp5) + Check((n + 5 - tmp5) / 5));
            ans = Math.Min(ans, C + D * tmp5 + Check((n - tmp5) / 5));
        }

        if (n % 3 == 0)
        {
            ans = Math.Min(ans, B + Check(n / 3));
        }
        else
        {
            ans = Math.Min(ans, B + D * (3 - tmp3) + Check((n + 3 - tmp3) / 3));
            ans = Math.Min(ans, B + D * tmp3 + Check((n - tmp3) / 3));
        }

        if (n % 2 == 0)
        {
            ans = Math.Min(ans, A + Check(n / 2));
        }
        else
        {
            ans = Math.Min(ans, D+A + Check((n + 1) / 2));
            ans = Math.Min(ans, D+A + Check((n - 1) / 2));
        }

        dic.Add(n, ans);
        return ans;
    }

}