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;
using System.Collections.Generic;

namespace Algorithm
{
    class Program
    {
        static void Main(string[] args)
        {
            var l = Console.ReadLine().Split().Select(long.Parse).ToArray();
            long A = l[0], B = l[1], C = l[2], D = l[3];
            var E = C * D / Gcd(C, D);

            var remStartC = A % C == 0 ? A : A + C - (A % C);
            var remStartD = A % D == 0 ? A : A + D - (A % D);
            var remStartE = A % E == 0 ? A : A + E - (A % E);
            var remEndC = B - (B % C);
            var remEndD = B - (B % D);
            var remEndE = B - (B % E);

            var diffC = (remEndC - remStartC) / C + 1;
            var diffD = (remEndD - remStartD) / D + 1;
            var diffE = (remEndE - remStartE) / E + 1;

            var total = B - A + 1;

            Console.WriteLine(total - (diffC + diffD - diffE));
        }

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