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)

package practice02;

import java.util.ArrayList;
import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        int T = 0;
        int piece = 0;
        int sum = 0;
        int sc[] = new int[5];
        ArrayList<Integer> array = new ArrayList<Integer>();

        Scanner scanT = new Scanner(System.in);
        Scanner scanLine = new Scanner(System.in);
        T = scanT.nextInt();

        for(int i = 0; i < T; i++){
        	sc[0] = scanLine.nextInt();
        	sc[1] = scanLine.nextInt();
        	sc[2] = scanLine.nextInt();
        	sc[3] = scanLine.nextInt();
        	sc[4] = scanLine.nextInt();

        	sum = sum++;
        	piece = piece + sc[4];

        	while(sum == sc[0]){
	        	if(sc[0] > sum * 5){
	            	sum = sum * 5;
	            	piece = piece + sc[3];
	        	}
	        	else if(sc[0] > sum * 3){
	            	sum = sum * 3;
	            	piece = piece + sc[2];
	        	}
	        	else if(sc[0] > sum * 2){
	            	sum = sum * 2;
	            	piece = piece + sc[1];
	        	}
	        	else if(sc[0] > sum){
	            	for(int j = sum; j < sc[0]; j++){
	                	sum = sum++;
	                	piece = piece + sc[4];
	            	}
	        	}
	        	else{
	            	for(int k = sum; k < sc[0]; k++){
	                	sum = sum--;
	                	piece = piece + sc[4];
	            	}
	        	}
        	}
        	array.add(piece);
        }
        for (int result : array) {
            System.out.println(result);
        }
    }
}