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: Accepted)

import java.io.*
import java.util.*
import java.lang.*
import java.lang.Math.*


fun solve() {
    val Q = rd.readInt()

    for (q in 0 until Q) {
        val (N, A, B, C, D) = rd.readListLong()

        val V = longArrayOf(2L, 3L, 5L)
        val W = longArrayOf(A, B, C)
        val memo = mutableMapOf<Long, Long>()

        fun dfs(n: Long): Long {
            if (n<=0L) return 0L

            if (memo.containsKey(n)) return memo[n]!!

            var res = if (LINF/D > n) n*D else LINF

            for (i in 0 until 3) {
                val l = (n/V[i])*V[i]
                res = min(res, dfs(l/V[i]) + W[i] + (n-l)*D)

                val r = ((n+V[i]-1)/V[i])*V[i]
                if (r/V[i] < n) {
                    res = min(res, dfs(r / V[i]) + W[i] + (r - n) * D)
                }
            }

            memo[n] = res

            return res
        }

        val ans = dfs(N)

        println(ans)
    }
}


//val rd = debug.Reader("agc", "044", "a", "sample-1")
val rd = Reader()


fun main(args: Array<String>) {
    try {
        var exception: Throwable? = null
        val sth = Thread(null, SolveThread(), "solveThread", 128 * 1024 * 1024)
        sth.setUncaughtExceptionHandler { _, e -> exception = e }
        sth.start(); sth.join()
        if (exception != null) throw exception!! }
    catch (e: Exception) { throw e }
    finally { rd.close() }
}
const val MOD = 1_000_000_007L; const val INF = Int.MAX_VALUE/2; const val LINF = Long.MAX_VALUE/2
data class IntPair(val first: Int, val second: Int)
val errPrintln: (Any) -> Unit = { msg -> System.err.println(msg) }
fun rAssert(exp: Boolean, lazyMsg: () -> String = {""}) {
    if (!exp) { val msg = lazyMsg(); errPrintln("EAssert Error: $msg"); throw Error(msg) }
}
fun tAssert(exp: Boolean, lazyMsg: () -> String = {""}) {
    if (!exp) { val msg = lazyMsg(); errPrintln("TAssert Error: $msg"); Thread.sleep(3000) }
}
class SolveThread : Runnable {
    override fun run() { solve() }
}
class Reader {
    private val br = BufferedReader(InputStreamReader(System.`in`))
    val readString: () -> String = { br.readLine() }
    val readInt: () -> Int = { br.readLine().toInt() }
    val readLong: () -> Long = { br.readLine().toLong() }
    val readDouble: () -> Double = { br.readLine().toDouble() }
    val readIntArray: () -> IntArray = { br.readLine().split(' ').map { it.toInt() }.toIntArray() }
    val readLongArray: () -> LongArray = { br.readLine().split(' ').map { it.toLong() }.toLongArray() }
    val readListInt: () -> List<Int> = { br.readLine().split(' ').map { it.toInt() } }
    val readListLong: () -> List<Long> = { br.readLine().split(' ').map { it.toLong() } }
    val readListStringCol: (Int) -> List<String> = { N -> (0 until N).map { readString() } }
    val readListIntCol: (Int) -> List<Int> = { N -> (0 until N).map { readInt() } }
    val readListIntCols: (Int) -> List<List<Int>> = { N -> (0 until N).map { br.readLine().split(' ').map { it.toInt() } } }
    val readListLongCol: (Int) -> List<Long> = { N -> (0 until N).map { readLong() } }
    val readListLongCols: (Int) -> List<List<Long>> = { N -> (0 until N).map { br.readLine().split(' ').map { it.toLong() } } }
    val close: () -> Unit = { br.close() }
    protected fun finalize() { close() }
}