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 int is_gcd(long long int a, long long int b);

int main(void){
  long long int a,b,c,d;
  scanf("%ld %ld %ld %ld",&a,&b,&c,&d);
  long long int lcm;
  long long int left, right;
  long long int c_num, d_num, cd_num;
  
  lcm = c*d/is_gcd(c,d);


  left = a/c; right = b/c;
  c_num = right - left + 1;
  if(a%c != 0)
    c_num--;    
  //printf("%ldで割り切れるのは%ld個\n",c,c_num);
  
  left = a/d; right = b/d;
  d_num = right - left + 1;
  if(a%d != 0)
    d_num--;
  //printf("%ldで割り切れるのは%ld個\n",d,d_num);
  
  left = a/lcm; right = b/lcm;
  cd_num = right - left + 1;
  if(a%lcm != 0)
    cd_num--;
  //printf("%ldで割り切れるのは%ld個\n",lcm,cd_num);

  long long int num = b - a + 1;
  
  printf("%ld\n",num - (c_num + d_num - cd_num) );

  return 0;
}


long long int is_gcd(long long int x, long long int y){
  long long int tmp,z;
  if(x<y){
    tmp = x;
    x = y;
    y = tmp;
  }
  z = x % y;
  while(z != 0){
    x = y;
    y = z;
    z = x % y;
  }
  return y;
}