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>
#include<stdlib.h>
#include<math.h>
#include<string.h>
long gcd(long a,long b){return b?gcd(b,a%b):a;}
long lcm(long a,long b){return a/gcd(a,b)*b;}
 
int main(void){
    long a,b,c,d,l,ans;
    scanf("%ld%ld%ld%ld",&a,&b,&c,&d);
    l = lcm(c,d);
    ans = (b-a+1) - ( b/c - (a-1)/c + b/d - (a-1)/d - b/l + (a-1)/l );
    printf("%ld\n",ans);
    return 0;
}