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++ (GCC 9.2.1) (judge verdict: Accepted)

#include <stdint.h>

#include <iostream>

using namespace std;

int64_t Gcd(int64_t a, int64_t b) {
  if (b == 0) return a;
  return Gcd(b, a % b);
}

int64_t Lcm(int64_t a, int64_t b) { return a / Gcd(a, b) * b; }

int64_t Cnt(int64_t a, int64_t b, int64_t x) {
  int64_t i = (a + x - 1) / x;
  int64_t j = b / x;
  return j - i + 1;
}

int main(void) {
  int64_t A, B, C, D;
  cin >> A >> B >> C >> D;

  cout << B - A + 1 - (Cnt(A, B, C) + Cnt(A, B, D) - Cnt(A, B, Lcm(C, D)))
       << endl;
  return 0;
}