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.IO;
using System.Linq;

namespace A
{
    public class Program
    {
        static void Main(string[] args)
        {
            var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            Console.SetOut(sw);
            Solve();
            Console.Out.Flush();
        }

        public static void Solve()
        {
            var t = int.Parse(Console.ReadLine());
            for (var i = 0; i < t; i++)
            {
                var nabcd = Console.ReadLine().Trim().Split(' ').Select(long.Parse).ToArray();
                var n = nabcd[0];
                var a = nabcd[1];
                var b = nabcd[2];
                var c = nabcd[3];
                var d = nabcd[4];

                var memo = new Dictionary<long, long>();
                memo[0] = 0;
                memo[1] = d;
                long Dfs(long x)
                {
                    if (memo.ContainsKey(x)) return memo[x];
                    var l2 = (x / 2) * 2;
                    var r2 = ((x + 1) / 2) * 2;
                    var l3 = (x / 3) * 3;
                    var r3 = ((x + 2) / 3) * 3;
                    var l5 = (x / 5) * 5;
                    var r5 = ((x + 4) / 5) * 5;
                    var tmp = (long)Math.Pow(10, 18);
                    if (x < tmp / d) tmp = x * d;
                    tmp = Math.Min(tmp, Math.Abs(l2 - x) * d + a + Dfs(l2 / 2));
                    tmp = Math.Min(tmp, Math.Abs(r2 - x) * d + a + Dfs(r2 / 2));
                    tmp = Math.Min(tmp, Math.Abs(l3 - x) * d + b + Dfs(l3 / 3));
                    tmp = Math.Min(tmp, Math.Abs(r3 - x) * d + b + Dfs(r3 / 3));
                    tmp = Math.Min(tmp, Math.Abs(l5 - x) * d + c + Dfs(l5 / 5));
                    tmp = Math.Min(tmp, Math.Abs(r5 - x) * d + c + Dfs(r5 / 5));
                    return memo[x] = tmp;
                }
                Console.WriteLine(Dfs(n));
            }
        }
    }
}