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

namespace contest_Csharp
{
    class Program
    {
        static long N = 0, A = 0, B = 0, C = 0, D = 0;
        static Dictionary<long, long> memo = new Dictionary<long, long>();


        static void Main(string[] args)
        {
            var sw = new System.IO.StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            Console.SetOut(sw);

            var vals = Console.ReadLine().Split(' ')
                .Select(x => int.Parse(x)).ToList();

            int T = vals[0];
            for (int i = 0; i < T; i++)
            {
                memo = new Dictionary<long, long>();
                var vals2 = Console.ReadLine().Split(' ')
                .Select(x => long.Parse(x)).ToList();
                N = vals2[0];
                A = vals2[1];
                B = vals2[2];
                C = vals2[3];
                D = vals2[4];
                var ans = serch(N);
                Console.WriteLine(ans);


            }



            Console.Out.Flush();

        }
        static long serch(long num)
        {
            checked
            {
                if (num == 900000000000000000)
                {

                }
                long ans;
                long gval;
                if (memo.TryGetValue(num, out gval))
                {
                    return gval;
                }
                if (num == 1)
                {
                    memo[num] = D;
                    return D;

                }
                if (num == 0)
                {
                    return 0;
                }
                ans = serch(num / 2) + A + D * (num % 2);
                
                if (num > 2)
                    ans = Math.Min(serch(num / 2 + 1) + A + D * (2-num % 2), ans);
                
                ans = Math.Min(serch(num / 3) + B + D * (num % 3), ans);
                ans = Math.Min(serch(num / 3 + 1) + B + D * (3 - num % 3), ans);
                ans = Math.Min(serch(num / 5) + C + D * (num % 5), ans);
                ans = Math.Min(serch(num / 5 + 1) + C + D * (5 - num % 5), ans);
                if (long.MaxValue / num > D)
                {
                    ans = Math.Min(ans, D * num);
                }

                memo[num] = ans;
                

                return ans;
            }
        }



    }

}