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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Linq;
using System.Collections;
using System.Collections.Generic;

class Program
{
    public static long Div(long A,long B)
    {
        if (A == 0)
            return 0;
        else
            return A / B;
    }

    public static void Main()
    {
        var s = Console.ReadLine().Split(' ');
        long A = long.Parse(s[0]);
        long B = long.Parse(s[1]);
        long C = long.Parse(s[2]);
        long D = long.Parse(s[3]);

        long dc = Div(B, C) - Div(A - 1, C);
        long dd = Div(B, D) - Div(A - 1, D);
        long dcom = Div(B, Lcm(C, D)) - Div(A - 1, Lcm(C, D));

        Console.WriteLine((B - A + 1) - (dc + dd - dcom));
    }

    public static long Lcm(long a, long b)
    {
        return a * b / Gcd(a, b);
    }
    
    public static long Gcd(long a, long b)
    {
        if (a < b)
            return Gcd(b, a);
        while (b != 0)
        {
            var remainder = a % b;
            a = b;
            b = remainder;
        }
        return a;
    }
}