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;
using System.Text;
using System.Threading.Tasks;

namespace ABC131C
{
    class Program
    {
        static void Main(string[] args)
        {
            var input = Console.ReadLine().Split(' ').Select(long.Parse).ToArray();

            var a = input[0];
            var b = input[1];
            var c = input[2];
            var d = input[3];

            var all = b - a + 1;

            var c1 = (a - 1) / c;
            var c2 = b / c;
            var c3 = c2 - c1;

            var d1 = (a - 1) / d;
            var d2 = b / d;
            var d3 = d2 - d1;

            var cd = Lcm(c, d);

            var cd1 = (a - 1) / cd;
            var cd2 = b / cd;
            var cd3 = cd2 - cd1;

            Console.WriteLine(all - (c3 + d3 - cd3));
        }

        static long Lcm(long a, long b)
        {
            return (a * b) / Gcd(a, b);
        }

        static long Gcd(long a, long b)
        {
            if (a == 0)
            {
                return b;
            }
            if (b == 0)
            {
                return a;
            }

            if (a > b)
            {
                a %= b;
                return Gcd(a, b);
            }
            else
            {
                b %= a;
                return Gcd(b, a);
            }
        }
    }
}