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 Kotlin (1.3.71) (judge verdict: Wrong Answer)

import java.lang.Exception
import kotlin.math.abs

fun solve(): Long {
    val input = readLine()!!.split(" ").map(String::toLong)
    val N = input[0];
    val A = input[1];
    val B = input[2];
    val C = input[3];
    val D = input[4];

    var minCost = Long.MAX_VALUE

    if (N == 1L) {
        return D
    }

    outeri@for(i in 0 until 100) {
        var pow2 = 1
        if (i==0) {
            pow2 = 1;
        } else if (i==1) {
            pow2 = 2;
        } else {
            pow2 = 2;
            for (z in 0 until i-1) {
                try {
                    pow2 = Math.multiplyExact(pow2, 2)
                } catch (e: Exception) {
                    break@outeri
                }
            }
        }

        outerj@for(j in 0 until 100) {
            var pow3 = 1
            if (j==0) {
                pow3 = 1;
            } else if (j==1) {
                pow3 = 3;
            } else {
                pow3 = 3;
                for (z in 0 until j-1) {
                    try {
                        pow3 = Math.multiplyExact(pow3, 3)
                    } catch (e: Exception) {
                        break@outerj
                    }
                }
            }

            outerk@for(k in 0 until 100) {
                var pow5 = 1
                if (k==0) {
                    pow5 = 1;
                } else if (k==1) {
                    pow5 = 5;
                } else {
                    for (z in 0 until k-1) {
                        pow5 = 5;
                        try {
                            pow5 = Math.multiplyExact(pow5, 5)
                        } catch (e: Exception) {
                            break@outerk
                        }
                    }
                }
                try {
                    var ci = i;
                    var cj = j;
                    var ck = k;

                    val t = Math.multiplyExact(Math.multiplyExact(pow2,pow3), pow5)
                    var l = abs(N-t)

                    // Dを足すコストのほうが低かったらこうかん？

                    val iA = Math.multiplyExact(ci.toLong(),A)
                    val jB = Math.multiplyExact(cj.toLong(),B)
                    val kC = Math.multiplyExact(ck.toLong(),C)
                    val lD = Math.multiplyExact(l, D)

                    val cost = Math.addExact(iA, Math.addExact(jB, Math.addExact(kC, lD)))


                    if (cost < minCost) {
                        minCost = cost
                    }
                } catch (e: Exception) {
                    break@outerk
                }
            }
        }
    }

    return minCost + D;
}


fun main(args: Array<String>) {
    val T = readLine()!!.toInt()
    repeat(T) {
        println(solve())
    }
}