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: Runtime Error)


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

class GFG
{
    static long a = 0, b = 0, c = 0, d = 0;
    static long
        target = 0;
    static Dictionary<string, long> dic = new Dictionary<string, long>();
    public static void Main()
    {
        var t = int.Parse(Console.ReadLine());
        while (t > 0)
        {
            t--;
            var input = Console.ReadLine().Split(' ');

            target = int.Parse(input[0]);
            a = int.Parse(input[1]);
            b = int.Parse(input[2]);
            c = int.Parse(input[3]);
            d = int.Parse(input[4]);
            var ans = PlayToWin(target);
        }

    }

    public static long PlayToWin(long x)
    {
        if (x == 1)
            return 1;
        if (x == 0)
            return 0;
        string key = x.ToString();
        if (dic.ContainsKey(key))
            return dic[key];
        long c2 = ((x + 1) / 2) * 2;
        long f2 = (x / 2) * 2;
        long c3 = ((x + 2) / 3) * 3;
        long f3 = (x / 3) * 3;
        long c5 = ((x + 4) / 5) * 5;
        long f5 = (x / 5) * 5;

        long ret = (x < 1000000000000000000 / d) ? x * d : 1000000000000000000;

        var ans1 = (c2 - x) * d + a + PlayToWin(c2 / 2);
        var ans2 = (x - f2) * d + a + PlayToWin(f2 / 2);
        var ans3 = (c3 - x) * d + b + PlayToWin(c3 / 3);
        var ans4 = (x - f3) * d + b + PlayToWin(f3 / 3);
        var ans5 = (c5 - x) * d + c + PlayToWin(c5 / 5);
        var ans6 = (x - f5) * d + c + PlayToWin(f5 / 5);

        dic.Add(key, Math.Min(Math.Min(Math.Min(Math.Min(Math.Min(Math.Min(ret, ans1), ans2), ans3), ans4), ans5), ans6));
        return dic[key];
    }

}