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<string.h>
#include<math.h>
#include <stdlib.h>

long long lmp(long long a, long long b) {
	long long upper, lower, r;

	if (a >= b)upper = a, lower = b;
	else upper = b, lower = a;
	r = upper % lower;
	if (r) lmp(lower, r);
	else return lower;
}

int main(void) {
	long long a, b, c, d;
	long long ans = 0;
	long long lcp_cd;

	scanf("%lld %lld %lld %lld", &a, &b, &c, &d);
	lcp_cd = c * d / lmp(c, d);
	//printf("lmp_cd=%lld\n", lcp_cd);

	ans += b / c;
	ans += b / d;
	ans -= b / lcp_cd;

	ans -= (a - 1) / c;
	ans -= (a - 1) / d;
	ans += (a - 1) / lcp_cd;

	printf("%lld", b - a + 1 - ans);
	return 0;
}