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.Collections;
using System.Linq;

namespace ProjectContest
{
    class Test
    {
        static void Main()
        {
            var abcd = Array.ConvertAll(Console.ReadLine().Split(), Convert.ToInt64);
            long a = abcd[0], b = abcd[1], c = abcd[2], d = abcd[3];
            long kq = b-a+1;
            long t1 = b / c - (a % c == 0 ? a / c : a / c + 1) + 1;
            long t2 = b / d - (a % d == 0 ? a / d : a / d + 1) + 1;
            long cd = BCNN(c, d);
            long t3= b / cd - (a % cd == 0 ? a / cd : a / cd + 1) + 1;
            Console.WriteLine(kq - t1 - t2 + t3);
        }

        private static long BCNN(long c, long d)
        {
            long x = c, y = d;
            while (c * d != 0)
            {
                if (c >= d) c %= d;
                else d %= c;
            }
            return x * y / (c + d);
        }
    }
}