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
# C - Anti-Division

fscanf(STDIN, "%d %d %d %d", $A, $B, $C, $D);

$A = $A - 1;

#1からA
$ADividedC = intdiv($A, $C);
$ADividedD = intdiv($A, $D);
$ADividedCD = intdiv($A, lcm($C, $D));    
$AA = ($A - $ADividedC - $ADividedD + $ADividedCD);

#1からB
$BDividedC = intdiv($B, $C);
$BDividedD = intdiv($B, $D);
$BDividedCD = intdiv($B, lcm($C, $D));
$BB = ($B - $BDividedC - $BDividedD + $BDividedCD);

echo ($BB - $AA) . PHP_EOL;

//最大公約数
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;
}
 
//最小公倍数
function lcm($m, $n){
    return $m * $n / gcd($m, $n);
}