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
// 入力
fscanf(STDIN, '%d %d %d %d', $a, $b, $c, $d);

$ans = 0;

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

$ans += $b - $a +1;
$ans -= intdiv($b, $c) - intdiv($a - 1, $c);
$ans -= intdiv($b, $d) - intdiv($a - 1, $d);
$ans += intdiv($b, $e) - intdiv($a - 1, $e);

echo $ans.PHP_EOL;

function gcd($m, $n){
    if($n > $m) list($m, $n) = [$n, $m];

    if ($m % $n === 0) return $n;
    else return gcd($n, $m % $n);
}

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