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)

/* Coached by Dukkha */
#include <stdio.h>

long long solve(long long a, long long b, long long c) {
	return b / c - (a - 1) / c;
}

int gcd(int a, int b) {
	return b == 0 ? a : gcd(b, a % b);
}

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

int main() {
	long long a, b;
	int c, d;

	scanf("%lld%lld%d%d", &a, &b, &c, &d);
	printf("%lld\n", b - a + 1 - solve(a, b, c) - solve(a, b, d) + solve(a, b, lcm(c, d)));
	return 0;
}