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
$T = intval(fgets(STDIN));
for($i = 0; $i < $T; $i++){
  [$N, $A, $B, $C, $D] = array_map('intval',explode(' ',trim(fgets(STDIN))));
  $memo = [];
  echo cost($N),PHP_EOL;
}
function cost($i){
  global $N, $A, $B, $C, $D, $memo;
  if($i == 0)return 0;
  if($i == 1)return $D;
  if(isset($memo[$i]))return $memo[$i];
  $min = abs($i)*$D;
  foreach(["A" => 2, "B" => 3, "C" => 5] as $c => $mod){
    $up = intdiv($i+$mod-1,$mod)*$mod;
    chmin($min, abs($up-$i)*$D+$$c+cost($up/$mod));
    $down = intdiv($i,$mod)*$mod;
    chmin($min, abs($down-$i)*$D+$$c+cost($down/$mod));
  }
  $memo[$i] = $min;
  return $min;
}

function chmin(&$a,$b){if($a>$b){$a=$b;return 1;}return 0;}