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 9.2.1) (judge verdict: Accepted)

#include<stdio.h>

long long int LCM(long long int,long long int );

int main(void){
    long long int a,b,c,d,s,x,y,z;

    scanf("%lld %lld %lld %lld",&a,&b,&c,&d);

    s = LCM(c,d);
    x = b / c - a / c;
    if(a % c == 0)x++;
    y = b / d - a / d;
    if(a % d == 0)y++;
    z = b / s - a / s;
    if(a % s == 0)z++;

    printf("%lld",b - a + 1 - x - y + z);

    return 0;
}

long long int LCM(long long int a,long long int b)
{
 
  long long int r, x, tmp;
 
  x = a * b;
 
  /* 自然数 a > b を確認・入替 */
  if(a<b){
    tmp = a;
    a = b;
    b = tmp;
  }
 
  /* ユークリッドの互除法 */
  r = a % b;
  while(r!=0){
    a = b;
    b = r;
    r = a % b;
  }
  return x / b;
}