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 11.0.6) (judge verdict: Runtime Error)

import java.util.Scanner;

public class Main {

  static String ans = "No";
  static int H = 0;
  static int W = 0;
  static char[][] maze;
  static boolean[][] reached;

  public static void main(String[] args) {
    Scanner sc = new Scanner(System.in);
    H = sc.nextInt();
    W = sc.nextInt();

    maze = new char[H][W];
    reached = new boolean[H][W];
    int[] start = new int[2];

    for (int i = 0; i < H; i++){
      String s = sc.next();
      for ( int j = 0; j < W; j++){
        maze[i][j] = s.charAt(j);
        if ( 's' == maze[i][j]){
          start[0] = i;
          start[1] = j;
        }

      }
    }

    solve(start[0],start[1], maze);

    System.out.println(ans);

  }

  private static void solve(int y, int x, char[][] maze) {

    if ( y < 0 || y >= H || x < 0 || x >= W || maze[y][x] == '#') return;
    if ( reached[y][x] ) return;
    if (maze[y][x] == 'g'){ ans = "Yes"; return; }

    reached[y][x] = true;

    solve(y+1, x, maze);
    solve(y-1, x, maze);
    solve(y, x-1, maze);
    solve(y, x+1, maze);

    return;

  }

}