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 5.4.1) (judge verdict: Accepted)

#include <stdio.h>

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

int main() {
  long long int a, b, lcm, ans, c, d;
  scanf("%lld %lld %lld %lld", &a, &b, &c, &d);
  lcm = c*d/gcd(c, d);
  ans = b-a+1;
  ans -= b/c - (a-1)/c;
  ans -= b/d -(a-1)/d;
  ans += b/lcm - (a-1)/lcm;
  printf("%lld\n", ans);
  return 0;
}