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)

//#define _GLIBCXX_DEBUG
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
#define rep(i, n) for (int i = 0; i < (n); i++)
#define all(v) v.begin(), v.end()
#define allr(v) v.rbegin(), v.rend()

ll a, b, c, d;

ll num_of_mul(ll n) {//a以上b以下でnで割り切れるものの数
  return b/n - (a+n-1)/n + 1;
}

int main() {
  cin >> a >> b >> c >> d;
  ll lcm = c*d/__gcd(c, d);
  ll ng = num_of_mul(c) + num_of_mul(d) - num_of_mul(lcm);
  cout << b-a+1 - ng << endl;
  return 0;
}