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 long f(long long a, long long b) {
    long long r, t;
  if(a<b){
    t = a;
    a = b;
    b = t;
  }
  r = a % b;
  while(r!=0){
    a = b;
    b = r;
    r = a % b;
  }
  return b;
}


int main(void){
    long long A, B, C, D, S, gcd, lcm;
    scanf("%lld %lld %lld %lld", &A, &B, &C, &D);
    S=B-A+1;
    S-=B/C-(A-1)/C;
    S-=B/D-(A-1)/D;
    gcd=f(C, D);
    lcm=C*D/gcd;
    S+=B/lcm-(A-1)/lcm;
    printf("%lld\n", S);
}