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;

public static class Common
{
    // ユークリッドの互除法により最大公約数を得る
    public static long GCD(long m, long n)
    {
        if (m < n)
        {
            return GCD(n, m);
        }

        while (n != 0)
        {
            var t = n;
            n = m % n;
            m = t;
        }
        return m;
    }

    public static long LCM(long m, long n)
    {
        return m * n / (GCD(m, n));
    }
}

public class Solution
{
    // [start, end]
    static long GetCount(long start, long end, long div)
    {
        start = (start + div - 1) / div * div;
        if (start > end)
        {
            return 0;
        }

        return 1 + (end - start) / div;
    }

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

        long c = GetCount(A, B, C);
        long d = GetCount(A, B, D);
        var lcm = Common.LCM(C, D);
        long cd = GetCount(A, B, lcm);

        long count = B - A + 1 - c - d + cd;

        Console.WriteLine(count);
    }
}