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
fscanf(STDIN, "%d %d %d %d", $a, $b, $c, $d);

$lcm = lcm($c, $d);

$a_lcm = intdiv($a-1, $lcm);
$b_lcm = intdiv($b, $lcm);
$x = $b_lcm - $a_lcm;

$a_c = intdiv($a-1, $c);
$b_c = intdiv($b, $c);
$y = $b_c - $a_c;    

$a_d = intdiv($a-1, $d);
$b_d = intdiv($b, $d);
$z = $b_d - $a_d; 

echo ($b - $a +1) - ($y + $z - $x);

function gcd($a, $b) {
     if ($b === 0){
        return $a; 
     }
    return gcd($b, $a % $b);
}

function lcm($a, $b) {
    return $a * $b / gcd($a, $b);
}

?>