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: Runtime Error)

import java.util.Scanner

object Main extends App {
  val sc = new Scanner(System.in)
  val T = sc.nextInt

  for (i <- 1 to T) {
    val N = sc.nextLong
    val A, B, C, D = sc.nextInt

    val dp = Array.fill((N / 10e9 + 1).toInt, 10e9.toInt)(Int.MaxValue)

    dp(0)(0) = 0
    for (i <- 0L until N) {
      def i1(x: Long = i): Int = (x / 10e9).toInt
      def i2(x: Long = i): Int = (x % 10e9).toInt

      if (i > 0) dp(i1(i-1))(i2(i-1)) = math.min(dp(i1(i-1))(i2(i-1)), dp(i1())(i2()) + D)
      dp(i1(i+1))(i2(i+1)) = math.min(dp(i1(i+1))(i2(i+1)), dp(i1())(i2()) + D)
      dp(i1(i*2))(i2(i*2)) = math.min(dp(i1(i*2))(i2(i*2)), dp(i1())(i2()) + A)
      dp(i1(i*3))(i2(i*3)) = math.min(dp(i1(i*3))(i2(i*3)), dp(i1())(i2()) + B)
      dp(i1(i*5))(i2(i*5)) = math.min(dp(i1(i*5))(i2(i*5)), dp(i1())(i2()) + C)
    }

    println(dp((N / 10e9).toInt)((N % 10e9).toInt))
  }
}