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>

long gcd(long m, long n){
	long temp;
	while (m % n != 0){
		temp = n;
		n = m % n;
		m = temp;
	}
	return n;
}

long lcm(long c, long d){
    return c * d / gcd(c, d);
}
int main(void){
    long a, b, c, d;
    scanf("%ld%ld%ld%ld", &a, &b, &c, &d);
    //(B-A-1) - (cで割れる数) - (dで割れる数) + (cでもdでも割れる = cとdの最小公倍数で割れる数)
    long e = lcm(c, d);
    long xc = (b / c) - ((a-1) / c);
    long xd = (b / d) - ((a-1) / d);
    long xe = (b / e) - ((a-1) / e);
    long ans = b - a + 1 - xc - xd + xe;
    printf("%ld\n", ans);
    return 0; 
}