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: Accepted)

using System.Linq;
using System.Security.Cryptography.X509Certificates;
using System.Text;
using System;
using System.Collections;
using System.Collections.Generic;
using System.Globalization;
using System.IO;
using System.Reflection.Metadata.Ecma335;
using System.Numerics;

namespace AtCoder
{
    class Program
    {

        const int BiggestMod = 1000000007;
        public static void Main()
        {

            var numSoltion = int.Parse(Console.ReadLine());
            var ans = new long[numSoltion];

            for (int quest = 0; quest < numSoltion; quest++)
            {

                var args = Console.ReadLine().Split(' ').Select(x => long.Parse(x)).ToArray();
                
                var num = args[0];
                var A = args[1];
                var B = args[2];
                var C = args[3];
                var D = args[4];
                var memo = new Dictionary<long, long>();

                ans[quest] = Solve(num);

                long Solve(long num)
                {

                    if (num == 1) return D;
                    else if (num == 0) return 0;
                    else if (memo.ContainsKey(num)) return memo[num];
                    else
                    {

                        long
                            Ard = (num >> 1) << 1,
                            Aru = ((num + 1) >> 1) << 1,
                            Brd = (num / 3) * 3,
                            Bru = ((num + 2) / 3) * 3,
                            Crd = (num / 5) * 5,
                            Cru = ((num + 4) / 5) * 5,
                            minimum = long.MaxValue,
                            buf;

                        if (num < minimum / D) minimum = num * D;

                        buf = Math.Abs(Ard - num) * D + A + Solve(Ard / 2);
                        if (buf < minimum) minimum = buf;
                        
                        buf = Math.Abs(Aru - num) * D + A + Solve(Aru / 2);
                        if (buf < minimum) minimum = buf;

                        buf = Math.Abs(Brd - num) * D + B + Solve(Brd / 3);
                        if (buf < minimum) minimum = buf;
                        
                        buf = Math.Abs(Bru - num) * D + B + Solve(Bru / 3);
                        if (buf < minimum) minimum = buf;

                        buf = Math.Abs(Crd - num) * D + C + Solve(Crd / 5);
                        if (buf < minimum) minimum = buf;
                        
                        buf = Math.Abs(Cru - num) * D + C + Solve(Cru / 5);
                        if (buf < minimum) minimum = buf;

                        memo.Add(num, minimum);

                        return minimum;

                    }
                }

            }

            foreach (var data in ans)
                Console.WriteLine(data);
        }

    }

}