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: Accepted)

import java.util.*;

public class Main {
	static HashMap<Long, Long> memo;
	static int A,B,C,D;
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		
		int T = sc.nextInt();
		
		for(int i=0; i<T; i++) {
			long N = sc.nextLong();
			A = sc.nextInt();
			B = sc.nextInt();
			C = sc.nextInt();
			D = sc.nextInt();
			
			memo = new HashMap<>();
			memo.put(0l, 0l);
			memo.put(1l, (long)D);
			
			System.out.println(solve(N));
		}
		
		sc.close();
	}
	
	static long solve(long N) {
		if(memo.get(N)!=null)
			return memo.get(N);
		long min = Long.MAX_VALUE;
		if(N < Long.MAX_VALUE/D)
			min = N*D;
		
		for(int i=-1; i<=1; i++) {
			if((N+i)%2==0)
				min = Math.min(min, solve((N+i)/2)+Math.abs(i)*D+A);
		}
		for(int i=-1; i<=1; i++) {
			if((N+i)%3==0)
				min = Math.min(min, solve((N+i)/3)+Math.abs(i)*D+B);
		}
		for(int i=-2; i<=2; i++) {
			if((N+i)%5==0)
				min = Math.min(min, solve((N+i)/5)+Math.abs(i)*D+C);
		}

		memo.put(N, min);
		return min;
	}
}