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 (Clang 3.8.0) (judge verdict: Accepted)

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

long gcc(long a,long b);

int main(void){
  long a,b,c,d,e,countc,countd,counte,sum,gc;
  char str[1000],*p;
  
  fgets(str,sizeof(str),stdin);
  p=strtok(str," \n");
  a=atol(p);
  p=strtok(NULL," \n");
  b=atol(p);
  p=strtok(NULL," \n");
  c=atol(p);
  p=strtok(NULL," \n");
  d=atol(p);
  e=c*d/gcc(c,d);
  
  countc=b/c-(a-1)/c;
  countd=b/d-(a-1)/d;
  counte=b/e-(a-1)/e;
  
  
  sum=b-a+1-countc-countd+counte;
  
  printf("%ld\n",sum);
  
  
  return 0;
}


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