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>
typedef long long ll;
using namespace std;

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

int main(int argc, char **argv)
{
   ios_base::sync_with_stdio(false);
   cin.tie(NULL);

#ifdef LOCAL_DEFINE
   freopen("in.txt", "r", stdin);
#endif

   ll a, b, c, d, cd;
   cin >> a >> b >> c >> d;
   cd = c * d / gcd(c, d);

   ll ans = 0;
   ans += b / c - (a - 1) / c;
   ans += b / d - (a - 1) / d;
   ans -= b / cd - (a - 1) / cd;

   cout << b - a + 1 - ans << '\n';

   return 0;
}