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: Wrong Answer)

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

class Program {
    static void Main (string[] args) {
        var inp = Console.ReadLine().Split(' ');
        int T = int.Parse(inp[0]);

        for(int i = 0;i < T;i++) {
            var inp2 = Console.ReadLine().Split(' ');
            long N = long.Parse(inp2[0]);
            int A = int.Parse(inp2[1]); //2x
            int B = int.Parse(inp2[2]); //3x
            int C = int.Parse(inp2[3]); //5x
            int D = int.Parse(inp2[4]); //+1-1

            long coin = D;
            List<long> prime = PrimeFactors(N);
            r(prime,ref coin,A,B,C,D);

            Console.WriteLine("{0}",coin);
        }
    }

    public static void r (List<long> _prime,ref long _coin,int A,int B,int C,int D) {
        for(int i = 0;i < _prime.Count;i++) {
            switch(_prime[i]) {
                case 2:
                _coin += A;
                break;

                case 3:
                _coin += B;
                break;

                case 5:
                _coin += C;
                break;

                default:
                _coin += D;
                r(PrimeFactors(_prime[i] - 1),ref _coin,A,B,C,D);
                break;
            }
        }
    }

    public static List<long> PrimeFactors (long n) {
        long i = 2;
        long tmp = n;
        List<long> tmpList = new List<long>();

        while(i * i <= n) {
            if(tmp % i == 0) {
                tmp /= i;
                tmpList.Add(i);
            } else {
                i++;
            }
        }

        if(tmp != 1) tmpList.Add(tmp);

        return tmpList;
    }
}