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 between(long long int a, long long int b, long long int c) {
	long long int lo = a/c, hi = b/c;
	if (a%c != 0) lo++;
	if (lo > hi) return 0;
	return hi-lo + 1;
}

long long int gcd(long long int a, long long int b) {
	while (b) {
		long long int t = b;
		b = a%b;
		a = t;
	}
	return a;
}

long long int lcm(long long int a, long long int b) {
	long long int g = gcd(a, b);
	return a*b / g;
}

int main(void) {
	long long int a, b, c, d;
	scanf("%lld%lld%lld%lld", &a, &b, &c, &d);

	long long int cnt = b-a + 1;
	cnt -= between(a, b, c);
	cnt -= between(a, b, d);
	cnt += between(a, b, lcm(c, d));
	printf("%lld\n", cnt);
}