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<iostream>
#include<vector>
#include<string>
#include<algorithm>
#include<cmath>
#include<functional>
#include<map>
#include<cstdlib>
#include<complex>
#include<numeric>

using namespace std;
using Int = long long;
Int INF = 1LL << 60;

Int gcd(Int a, Int b) { return b ? gcd(b, a % b) : a; }

int main() {

	Int a, b, c, d;
	cin >> a >> b >> c >> d;

	Int temp_c = 0;
	Int temp_d = 0;
	Int temp_cd = 0;
	Int cd = c*d/gcd(c, d);

	//1-B
	temp_c = b / c;
	temp_d = b / d;
	temp_cd = b / cd;

	//A-B
	temp_c -= (a - 1) / c;
	temp_d -= (a - 1) / d;
	temp_cd -= (a - 1) / cd;

	Int ans = (b - a + 1) - temp_c - temp_d + temp_cd;

	cout << ans << endl;
}