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 Scala (2.13.1) (judge verdict: Accepted)

import java.io.{BufferedOutputStream, BufferedReader, InputStreamReader, PrintWriter}

import scala.collection.mutable

object Main {
  def main(args: Array[String]): Unit = {
    val in = new BufferedReader(new InputStreamReader(System.in))
    val out = new PrintWriter(new BufferedOutputStream(System.out))
    val t = in.readLine().toInt

    case class Elem(value: Long, cost: Long)

    def minCost(n: Long, a: Int, b: Int, c: Int, d: Int): BigInt = {
      val memo = mutable.HashMap.empty[Long, BigInt]
      memo.update(0L, 0L)
      memo.update(1L, d)

      def inner(n: Long): BigInt = {
        memo.getOrElseUpdate(n,
          List(
            BigInt(d) * n,
            BigInt(d) * (n - n / 5 * 5) + c + inner(n / 5),
            BigInt(d) * ((n + 4) / 5 * 5 - n) + c + inner((n + 4) / 5),
            BigInt(d) * (n - n / 3 * 3) + b + inner(n / 3),
            BigInt(d) * ((n + 2) / 3 * 3 - n) + b + inner((n + 2) / 3),
            BigInt(d) * (n - n / 2 * 2) + a + inner(n / 2),
            BigInt(d) * ((n + 1) / 2 * 2 - n) + a + inner((n + 1) / 2)
          ).min
        )
      }

      inner(n)
    }

    for (_ <- 0 until t) {
      val (n, a, b, c, d) = in.readLine().split("\\s+") match {
        case Array(n, a, b, c, d) => (n.toLong, a.toInt, b.toInt, c.toInt, d.toInt)
      }
      out.println(minCost(n, a, b, c, d))
    }

    out.flush()
  }
}