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 PHP (7.4.4) (judge verdict: Accepted)

<?php
                            //4 9 2 3
    fscanf(STDIN,"%d%d%d%d",$A,$B,$C,$D);
    
    $ansx=0;
    $ansy=0;
    //$B以下の整数で$c,$d,lcm($c,$d)で割り切れるものの個数を求める
    $ansx += intdiv($B,$C);
    $ansx += intdiv($B,$D);
    $ansx -= intdiv($B,lcm($C,$D));
    $ansy += intdiv(($A-1),$C);
    $ansy += intdiv(($A-1),$D);
    $ansy -= intdiv(($A-1),lcm($C,$D));

    echo ($B-($A-1))-($ansx-$ansy);
    
    function lcm($m, $n){
        return $m * $n / gcd($m, $n);
    }
    function gcd($m,$n){
        //$mが大きい値にしておきたい
        if($n>$m)list($m,$n)=array($n,$m);
        
        //余りが0になるまで割り続けるような
        //計算をする。
        while($n != 0){
            $tmp_n = $n;
            $n = $m % $n;
            $m = $tmp_n;
        }
        return $m;
    }
    
?>