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);

printf("%d", countN(1) - countN($c) - countN($d) + countN(lcm($c,$d)));

function countN($div){
  global $a, $b;
  return intdiv($b, $div) - intdiv($a-1, $div);
}

function gcd($m, $n){
    if(!$n)return abs($m);
    return gcd($n, $m % $n);
}
function lcm($a, $b) {
    return $a / gcd($a, $b) * $b;
}