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 Java (OpenJDK 1.8.0) (judge verdict: Runtime Error)

import java.lang.reflect.Array;
import java.util.*;

public class Main {

  public static void main(String[] args) {
    Scanner sc = new Scanner(System.in);
    int tests = sc.nextInt();
    long[] results = new long[tests];
    for (int t = 0; t < tests; t++) {
      long N = sc.nextLong();
      long A = sc.nextLong();
      long B = sc.nextLong();
      long C = sc.nextLong();
      long D = sc.nextLong();
      long x = 1;
      long currPrice = D;
      results[t] = coinHelper(N, A, B, C, D, x, currPrice);
    }
    for (int t = 0; t < tests; t++) {
      System.out.println(results[t]);
    }
  }


  static long coinHelper(long N, long A, long B, long C, long D, long x, long currPrice) {


    if (x >= N) {
      return Math.min(Long.MAX_VALUE, currPrice + (x - N) * D);
    }

    long copyPrice = Math.min(Long.MAX_VALUE, currPrice);
    long cx = Math.min(Long.MAX_VALUE, x);
    long m2 = coinHelper(N, A, B, C, D, Math.min(cx * 2, Long.MAX_VALUE), Math.min(copyPrice + A, Long.MAX_VALUE));
    long m3 = coinHelper(N, A, B, C, D, Math.min(cx * 3, Long.MAX_VALUE), Math.min(copyPrice + B, Long.MAX_VALUE));
    long m5 = coinHelper(N, A, B, C, D, Math.min(cx * 5, Long.MAX_VALUE), Math.min(copyPrice + C, Long.MAX_VALUE));
    long i1 = coinHelper(N, A, B, C, D, Math.min(cx + 1, Long.MAX_VALUE), Math.min(copyPrice + D, Long.MAX_VALUE));
    long[] arr = {m2, m3, m5, i1};
    Arrays.sort(arr);
    return arr[0];
  }
}