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 <vector>
#include <list>
#include <map>
#include <string>
#include <iostream>
#include <fstream>
#include <algorithm>
#include <cmath>
#include <utility>

using namespace std;
typedef long long ll;
typedef long double ld;

ll solve(void);

int main(void)
{
	while (solve())
	{
	}
	return 0;
}

ll hoge(ll x, ll y)
{
	if (x % y == 0) {
		return y;
	}
	if (x == 1) return 1;
	return hoge(y, x % y);
}

ll solve(void)
{
	ll a, b, c, d;
	cin >> a >> b >> c >> d;

	ll gcd = hoge(c,d);
	ll lcm = c * d / gcd;

	ll da = a - 1 - ((a-1)/c + (a-1)/d - (a-1)/(lcm));
	ll db = b - (b/c + b/d - b/lcm);

	cout << db - da << endl;


	return 0;
}