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>
using namespace std;
typedef long long ll;

ll gcd(ll a, ll b) {
  if (b == 0) return a;
  else return gcd(b, a % b);
}

int main() {
  ll A, B, C, D;
  cin >> A >> B >> C >> D;
  A -= 1;
  ll X = (B - B / C - B / D + B / (C * D / gcd(C, D)));
  ll Y = (A - A / C - A / D + A / (C * D / gcd(C, D)));
  cout << X - Y << endl;
}