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 C++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#include<iostream>
#include<string>
#include <algorithm>
#include <functional>
using namespace std;

struct coin {
	int A, B, C, D;
	long N;
	struct coin *next;
 }*head,*now;
int main()
{	
	int T;
	head = NULL;

	//string input;
	//cout << "文字列を入力してください。" << endl;
	struct coin *ctemp;
	cin >> T;
	for (int i = 0; i < T; i++) {
		ctemp = new struct coin ;
		cin >> ctemp->N;
		cin >> ctemp->A;
		cin >> ctemp->B;
		cin >> ctemp->C;
		cin >> ctemp->B;
		ctemp->next = NULL;

		if (head == NULL) {
			head = ctemp;
		}
		else {
			now->next = ctemp;
		}
		now = ctemp;

	}
	double R[4];
	long ans, sum;
	now = head;
	for (int i = 0; i < T; i++) {
		R[0] = now->A / 2;
		R[1] = now->B / 3;
		R[2] = now->C / 5;
		ans = 1;
		sum = 1;

		while (1) {
			R[3] = sum * now->D;
			if (R[0] + R[1] < R[2]) {
				if (sum * 6 < now->N) {
					ans += now->A + now->B;
					sum = sum * 6;
				}
			}
			else if (R[2] < R[0]*2) {
				if (sum * 5 < now->N) {
					ans += now->C;
					sum = sum * 5;
				}
			}
			else if (R[0] * 2 < R[1]) {
				if (sum * 4 < now->N) {
					ans += now->A*2;
					sum = sum * 4;
				}
			}
			else if (R[1] < R[0]) {
				if (sum * 3 < now->N) {
					ans += now->B;
					sum = sum * 3;
				}
			}
			else if (R[0] < R[3]) {
				if (sum * 2 < now->N) {
					ans += now->A;
					sum = sum * 2;
				}
			}
			else {
				if (sum + 1 < now->N) {
					ans += now->D;
					sum = sum + 1;
				}
			}
			if (sum >= now->N) {
				break;
			}
		}
		cout << ans << endl;
	}

	//cout << input << "と入力されました。" << endl;
	return 0;
}