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 PHP (7.4.4) (judge verdict: Accepted)

<?php
// A
fscanf(STDIN, '%d', $T);
for ($t  = 0; $t < $T; $t++) {
    fscanf(STDIN, '%d %d %d %d %d', $N, $A, $B, $C, $D);
    $memo = [0, $D];
    $ans[] = f($N);
}
echo implode(PHP_EOL, $ans);

function f($num)
{
    global $memo, $A, $B, $C, $D;

    if (isset($memo[$num])) return $memo[$num];

    $c = $num * $D;
    foreach ([[2, $A], [3, $B], [5, $C]] as $arr) {
        list($x, $X) = $arr;
        $next_num = intdiv($num, $x);
        $move = $num % $x;
        $c = min($c, $X + $move * $D + f($next_num));
        if ($move > 0) $c = min($c, $X + ($x - $move) * $D + f($next_num + 1));
    }

    $memo[$num] = $c;
    return $memo[$num];
}