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: Accepted)

<?php
  
$abcd = explode(' ', trim(fgets(STDIN)));
$a = $abcd[0];
$b = $abcd[1];
$c = $abcd[2];
$d = $abcd[3];
 
$ac = intdiv($a-1,$c);
$bc = intdiv($b,$c);
$cx = $bc - $ac;
 
$ad = intdiv($a-1,$d);
$bd = intdiv($b,$d);
$dx = $bd - $ad;
 
$cd = lcm($c, $d);
$acd = intdiv($a-1,$cd);
$bcd = intdiv($b,$cd);
$abx = $bcd - $acd;
 
$ans = $b - $a + 1 - $cx - $dx + $abx;
echo intval($ans);
 
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);
}
 
  
?>