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);
$a--;
$e = lcm($c, $d);
$x = intdiv($b, $c) - intdiv($a, $c);
$y = intdiv($b, $d) - intdiv($a, $d);
$z = intdiv($b, $e) - intdiv($a, $e);
echo $b - $a - $x - $y + $z;

function lcm($n, $m){
	return $n * $m / gcd($n, $m);
}
function gcd($n, $m) {
	return $n % $m ? gcd($m, $n % $m) : $m;
}