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

public class Main {

    public static void main(String[] args) {
        Scanner scan=new Scanner(System.in);
        int times=scan.nextInt();
        for (int i = 0; i <times ; i++) {

            long target = scan.nextLong();
            long multi2 = scan.nextLong();
            long multi3 = scan.nextLong();
            long multi5 = scan.nextLong();
            long step1 = scan.nextLong();

            MyMap map = new MyMap();
            NextNums nextNums = new NextNums();
            nextNums.put(target, 0);
            map.put(target, 0L);


            while (!nextNums.isEmpty()) {
                NextNums tempNums = new NextNums();
                for (Long num : nextNums.map.keySet()) {
                    long cost = nextNums.map.get(num);
                    map.put(0,  cost+num*step1);
                    for (int off = -5; off <= 5; off++) {
                        long tempCost = Math.abs(off) * step1;
                        if (num + off < 6) {
                            map.put(num + off, tempCost + cost);
                        }
                        if (num + off > 0) {
                            if ((num + off) % 2 == 0) {
                                long newCost = cost + tempCost + multi2;
                                long newNum = (num + off) / 2;
                                if (newNum > 0) {
                                    if (map.put(newNum, newCost)) {
                                        tempNums.put(newNum, newCost);
                                    }
                                }
                            }
                            if ((num + off) % 3 == 0) {
                                long newCost = cost + tempCost + multi3;
                                long newNum = (num + off) / 3;
                                if (newNum > 0) {
                                    if (map.put(newNum, newCost)) {
                                        tempNums.put(newNum, newCost);
                                    }
                                }
                            }
                            if ((num + off) % 5 == 0) {
                                long newCost = cost + tempCost + multi5;
                                long newNum = (num + off) / 5;
                                if (newNum > 0) {
                                    if (map.put(newNum, newCost)) {
                                        tempNums.put(newNum, newCost);
                                    }
                                }
                            }
                        }
                    }
                }
                nextNums = tempNums;
            }
            System.out.println(map.out());
        }
    }
}

class MyMap{
    HashMap<Long,Long> map=new HashMap<>();
    public boolean put(long num,long cost){
        boolean ret=false;
        if(num>=0 && cost>=0) {
            if (!map.containsKey(num)) {
                map.put(num, cost);
                ret = true;
            } else {
                if (map.get(num) > cost) {
                    map.put(num, cost);
                    ret = true;
                }
            }
        }
        return ret;
    }
    public long out(){
        if (map.containsKey(0L)){
            return map.get(0L);
        }else {
            return 0;
        }
    }
}

class NextNums{
    HashMap<Long,Long> map=new HashMap<>();
    void put(long num,long cost){
        if (!map.containsKey(num)){
            map.put(num,cost);
        }else{
            if(map.get(num)>cost){
                map.put(num,cost);
            }
        }
    }
    boolean isEmpty(){
        return map.isEmpty();
    }
}