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.util.*
import kotlin.math.abs

fun main() = AGC044A.main()

object AGC044A {
    fun log(message: Any?) {
        println(message)// TODO: ←消す
    }

    class Case(
        val N: Long,
        val A: Int,
        val B: Int,
        val C: Int,
        val D: Int
    )

    data class Problem(val case: Case, val n: Long)

    fun main() {
        val T = readInt()
        val cases = (1..T).map {
            val (n, a, b, c, d) = readLongs()
            Case(N = n, A = a.toInt(), B = b.toInt(), C = c.toInt(), D = d.toInt())
        }

        val table = LazyMap<Problem, Long> { p ->
            val n = p.n
            when (n) {
                0L -> 0L
                1L -> p.case.D.toLong()
                else -> {
                    listOf(2, 3, 5).flatMap { k ->
                        val divCost = when (k) {
                            2 -> p.case.A
                            3 -> p.case.B
                            else -> p.case.C
                        }
                        val right = n / k
                        val left = (right + 1).takeIf { n % k != 0L } ?: right

                        val midRight = right * k
                        val midLeft = left * k

                        val D = p.case.D
                        val leftProblem = Problem(p.case, left)
                        val rightProblem = Problem(p.case, right)
                        listOf(
                            abs(n - left) * D + get(leftProblem),
                            abs(n - midLeft) * D + divCost + get(leftProblem),
                            abs(n - midRight) * D + divCost + D + get(leftProblem),
                            abs(n - right) * D + get(rightProblem),
                            abs(n - midRight) * D + divCost + get(rightProblem),
                            abs(n - midLeft) * D + divCost + D + get(rightProblem)
                        ).filter { it >= 0 }
                    }.min()!!
                }
            }
        }

        cases.forEach { case ->
            val ans = table[Problem(case, case.N)]
            println(ans)
        }
    }


    /*####################################################################################*/

    class LazyMap<K, V>(capacity: Int = 65536, private val init: LazyMap<K, V>.(K) -> V) {
        private val memo = HashMap<K, V>(capacity)
        operator fun get(key: K): V {
            return memo[key] ?: init(key).memorizingAt(key)
        }

        private fun V.memorizingAt(key: K): V {
            memo[key] = this
            return this
        }
    }

    fun readString() = readLine()!!
    fun readStrings() = readLine()!!.split(" ")
    fun readInt() = readLine()!!.toInt()
    fun readInts() = readLine()!!.split(" ").map { it.toInt() }
    fun readLong() = readLine()!!.toLong()
    fun readLongs() = readLine()!!.split(" ").map { it.toLong() }
    fun readMatrixRows(height: Int) = (1..height).map { readLine()!!.toList() }

    fun Boolean.yesOrNo() = if (this) "Yes" else "No"
    fun Double.toNaturalExpr() = println("%f".format(this))
}