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 Perl (v5.18.2) (judge verdict: Wrong Answer)

use strict;
use warnings;

my ($a, $b, $c, $d) = split /\s/, <>;

my $g = gcd($c, $d);
my $cd = $c * $d / $g;

my $div_c =  div_num($a, $b, $c);
my $div_d =  div_num($a, $b, $d);
my $div_cd =  div_num($a, $b, $cd);

my $num = $b - $a + 1;
my $div = $div_c + $div_d - $div_cd;

print $num - $div, "\n";

sub div_num {
	my ($s, $e, $d) = @_;
	my $s2 = $s + ($s % $d);
	if ($s2 < 0) {
		return 0;
	}
	
	my $num = $e - $s2 + 1;
	return int(($num - 1) / $d) + 1;
}

sub gcd {
	my ($a, $b) = @_;
	my $c = $a % $b;
	return $b if $c == 0;
	return gcd($b, $c);
}