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;

namespace ABC131_C
{
    class Program
    {
        static void Main(string[] args)
        {
            var ABCD = Console.ReadLine().Split().Select(long.Parse).ToArray();
            var A = ABCD[0];
            var B = ABCD[1];
            var C = ABCD[2];
            var D = ABCD[3];

            var fac1 = B / C - (A - 1) / C;
            var fac2 = B / D - (A - 1) / D;
            var fac3 = B / lcm(new long[2] { C, D }) - (A - 1) / lcm(new long[2] { C, D });

            Console.WriteLine(B - (A - 1) - fac1 - fac2 + fac3);
        }

        private static long lcm(long[] t)
        {
            var lcm = t[0];
            for (int i = 1; i < t.Length; i++)
            {
                lcm = lcm / gcd(lcm, t[i]) * t[i];
            }

            return lcm;
        }

        public static long gcd(long x, long y)
        {
            return (y == 0) ? x : gcd(y, (x % y));
        }
    }
}