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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
// #include <algorithm>

using namespace std;

long long gcd(long long a, long long b) { // Greatest Common Denominator - Euclidean Algorithm
	if (b == 0) return a;
	return gcd(b, a % b);
}

long long lcm(long long a, long long b) { // Lowest Common Multiple
	return (a * b) / gcd(a, b);
}

long long solve(long long x, long long c, long long d) { 
	return x - x / c - x / d + x / lcm(c, d);
}

int main() {
	
	long long A, B, C, D; 
	cin >> A >> B >> C >> D;

	long long b = B - B / C - B / D + B / lcm(C, D); 
	// // removes multiples of B and C and takes care of the duplicates for numbers <= A-1
	long long a =  A - 1 - (A - 1) / C - (A - 1) / D + (A - 1) / lcm(C, D);
	cout << b - a;
	// cout << solve(B, C, D) - solve(A - 1, C, D);
	return 0;
}