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 PHP7 (7.0.15) (judge verdict: Wrong Answer)

<?php
  fscanf(STDIN,"%d%d%d%d", $a,$b,$c,$d);
  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);
  }
  
  $cd = lcm($c,$d);
  
  $a--;
  if($c>$b && $d>$b){
      echo $b-$a;
      exit;
  }
  
  $count1 = (int)($b/$c)-(int)($a/$c);
  $count2 = (int)($b/$d)-(int)($a/$d);
  $count3 = (int)($b/$cd)-(int)($a/$cd);
  echo ($b-$a)-($count1+$count2-$count3);