Problem:
Score : 300 points

Problem Statement

You are given four integers A, B, C, and D. Find the number of integers between A and B (inclusive) that can be evenly divided by neither C nor D.

Constraints

1\leq A\leq B\leq 10^{18}

1\leq C,D\leq 10^9

All values in input are integers.

Input

Input is given from Standard Input in the following format:

A B C D

Output

Print the number of integers between A and B (inclusive) that can be evenly divided by neither C nor D.

Sample Input 1

4 9 2 3

Sample Output 1

2

5 and 7 satisfy the condition.

Sample Input 2

10 40 6 8

Sample Output 2

23

Sample Input 3

314159265358979323 846264338327950288 419716939 937510582

Sample Output 3

532105071133627368

Solution in PHP (5.6.30) (judge verdict: Wrong Answer)

<?php
fscanf(STDIN, "%d %d %d %d", $a, $b, $c, $d);
$c_c = floor($b / $c) - floor(($a - 1) / $c);
$d_c = floor($b / $d) - floor(($a - 1) / $d);
$cd_lcm = lcm($c, $d);
$cd_c = floor($b / $cd_lcm) - floor(($a - 1) / $cd_lcm);
echo $b - $a + 1 - ($c_c + $d_c - $cd_c);

function gcd($m, $n){
  if($n > $m) list($m, $n) = array($n, $m);   
  while($n !== 0){
    $tmp_n = $n;
    $n = $m % $n;
    $m = $tmp_n;
  }
  return $m;
}
function lcm($m, $n){
  return $m * $n / gcd($m, $n);
}
?>