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

long gcd(long a, long b){
  long t;
  if(a>b){t=a; a=b; b=t;}
  t=b%a;
  while(t!=0){
    b=a;
    a=t;
    t=b%a;
  }
  return a;
}

int main(void){
  long a, b;
  int c, d;
  scanf("%ld%ld%d%d", &a, &b, &c, &d);
  long l = ((long)c)*d/gcd(c, d);
  long x = b - b/c - b/d + b/l;
  a--; long y = a - a/c - a/d + a/l;
  printf("%ld\n", x-y);
}