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)

// 16:32 - 17:04
#include <iostream>

using ll = long long;

#define rep(i, n) for (int i = 0; i < (int)(n); ++i)

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

ll lcm(ll a, ll b) { return a / gcd(a, b) * b; }

ll f(ll x, ll c, ll d) {
  ll res = x;
  res -= x / c;
  res -= x / d;
  res += x / lcm(c, d);
  return res;
}

int main() {
  ll a, b, c, d;
  std::cin >> a >> b >> c >> d;

  ll ans = f(b, c, d) - f(a - 1, c, d);
  std::cout << ans << '\n';

  return 0;
}