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.Collections.Generic;
using System.Linq;

namespace CsTest
{
    public class Program
    {
        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;
        }

        static void Main(string[] args)
        {
                string[] line = Console.ReadLine().Split(' ');
                long A = long.Parse(line[0])-1, B = long.Parse(line[1]);
                long C = long.Parse(line[2]), D = long.Parse(line[3]);
                long lcm = Lcm(C, D);
                Console.WriteLine((B-A)-((B / C) + (B / D) - (A / C) - (A / D) - (B / lcm) + (A / lcm)));
        }
    }
}