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 <stdio.h>
#include <stdlib.h>

long gcd(long x, long y) {
  if (y == 0) {
    return x;
  } else {
    return gcd(y, x % y);
  }
}

long num_divisible(long n, long k) { return n / k; }

int main(int argc, char *argv[]) {
  // read inputs
  long A, B, C, D;
  scanf("%ld %ld %ld %ld", &A, &B, &C, &D);

  // solve
  long g = C / gcd(C, D) * D;

  printf("%ld\n",
         (B - num_divisible(B, C) - num_divisible(B, D) + num_divisible(B, g)) -
             (A - 1 - num_divisible(A - 1, C) - num_divisible(A - 1, D) +
              num_divisible(A - 1, g)));

  return 0;
}