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: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Linq;
using static System.Math;
class MainClass
{
    static long N, A, B, C, D;
    static Dictionary<long, long> Dic = new Dictionary<long, long>();
    static void Main()
    {
        var T = int.Parse(Console.ReadLine());
        for(int i = 0; i < T; i++)
        {
            var r = Console.ReadLine().Split().Select(long.Parse).ToArray();
            N = r[0];A = r[1];B = r[2];C = r[3];D = r[4];
            Dic = new Dictionary<long, long>();
            Dic[N] = 0;
            DFS(N, 0);
            Console.WriteLine(Dic[1] + D);
        }
    }

    static void DFS(long n,long m)
    {
        
        Dic[n] = Min(Dic[n], m);
        if (n <= 1) return;
        if (Dic[n] != m) return;

        long p = n % 2;
        if (Point(n / 2) > m + A + D * p)
            DFS(n / 2, Min(m + A + D * p,m + f(n-n/2,D)));
        if (p > 0)
        {
            long min = Min(m + A + D * (2 - p), m + f(n - n / 2 - 1, D));
            if ( Point(n / 2 + 1) > min)
                DFS(n / 2 + 1, min);
        }
        
         p = n % 3;
        if (Point(n / 3) > m + B + D * p)
            DFS(n / 3, Min(m + B + D * p,m + f(n-n/3,D)));
        if (p > 0)
        {
            long min = Min(m + B + D * (3 - p), m + f(n - n / 3 - 1, D));
                if(p>0&&Point(n/3+1)> min)
                    DFS(n / 3 + 1, min);
        }
        

        if (n < 5) return;
        p = n % 5;
        if (Point(n / 5) > m + C + D * p)
            DFS(n / 5, Min(m + C + D * p,m + f(n-n/5,D)));
        if (p > 0)
        {
            long min = Min(m + C + D * (5 - p), m + f(n - n / 5 - 1, D));
                if (p > 0 && Point(n / 5 + 1) >min)
                    DFS(n / 5 + 1,min);
        }
        
    }
    static long Point(long num)
    {
        if (!Dic.ContainsKey(num)) Dic[num] = long.MaxValue/2;
        return Dic[num];
    }
    static long f(long a,long b)
    {
        if( Log10(a)+Log10(b)+2>= 19)
        {
            return long.MaxValue/2;
        }
        return a * b;
    }
}