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
//error_reporting(0);
//$N = trim(fgets(STDIN));
list($A,$B,$C,$D) =  explode(" ",trim(fgets(STDIN)));
//$a =  explode(" ",trim(fgets(STDIN)));

printf("%d\n",calc($B,$C,$D)-calc($A-1,$C,$D));

function calc($x,$c,$d) {
  $ret = $x;
  $ret -= intdiv($x,$c);
  $ret -= intdiv($x,$d);
  $ret += intdiv($x,lcm($c,$d));
  return $ret;
}

function gcd($a,$b) {
  if ($b == 0) return $a;
  return gcd($b,$a%$b);
}
function lcm($a,$b) {
  $l = gcd($a,$b);
  return $a / $l * $b;
}