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: Accepted)

import java.util.HashMap;
import java.util.Map;
import java.util.Scanner;

public class Main {
	static long rec(long N , long A , long B , long C , long D , Map<Long, Long> memo){
		if(memo.containsKey(N)){
			return memo.get(N);
		}
		if(N == 0){
			return 0;
		}
		if(N == 1){
			return D;
		}
		long r5 = N / 5;
		long diff = N - r5 * 5;
		long ret = rec(r5 , A , B , C , D , memo) + D * diff + C;
		if(diff != 0){
			diff = (r5 + 1) * 5 - N;
			ret = Math.min(rec(r5 + 1 , A , B , C , D , memo) + D * diff + C , ret);
		}
		long r3 = N / 3;
		diff = N - r3 * 3;
		ret = Math.min(ret, rec(r3 , A , B , C , D , memo) + D * diff + B);
		if(diff != 0){
			diff = (r3 + 1) * 3 - N;
			ret = Math.min(ret, rec(r3 + 1 , A , B , C , D , memo) + D * diff + B);
		}
		long r2 = N / 2;
		diff = N - r2 * 2;
		ret = Math.min(ret, rec(r2 , A , B , C , D , memo) + D * diff + A);
		if(diff != 0){
			diff = (r2 + 1) * 2 - N;
			ret = Math.min(ret, rec(r2 + 1 , A , B , C , D , memo) + D * diff + A);
		}
		if(N < ret / D){
			ret = Math.min(ret, N * D);			
		}
		memo.put(N, ret);
		return ret;
	}
	static long solve(long N , long A , long B , long C , long D){
		Map<Long, Long> memo = new HashMap<Long, Long>();		
		return rec(N , A , B , C , D , memo);
	}
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int T = sc.nextInt();
		for(int cn = 1 ; cn <= T ; ++cn){
			long N = sc.nextLong();
			long A = sc.nextLong();
			long B = sc.nextLong();
			long C = sc.nextLong();
			long D = sc.nextLong();
			long ret = solve(N , A , B , C , D);
			System.out.println(ret);
		}
	}
}