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>

typedef long long ll;

ll gcd(ll a, ll b);
long long lcm(long long a, long long b);
long long gD(long long a, long long b, long long c);


int main()
{	
	long long a, b, c, d, diff, ans;
	
	scanf("%lld %lld %lld %lld", &a, &b, &c, &d);
	
	diff = b-a+1;
	ans = diff - (gD(a, b, c) + gD(a, b, d) - gD(a, b, lcm(c, d)));
	//printf("%lld, %lld, %lld, %lld\n", diff, gD(a, b, c), gD(a, b, d), gD(a, b, lcm(c, d)));
	printf("%lld\n", ans);
	return 0;
}



ll gcd(ll a, ll b)
{
	if (!b) return a;
	if(!a) return b;
	
	a = a%b;
	return gcd(b, a);
}


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


long long gD(long long a, long long b, long long c)
{
	if (a%c) a = ( ( a / c ) + 1 ) * c;
	if (b%c) b = ( b / c ) * c;
	
	//printf("[*] inside gD: %lld %lld for %lld\n", a, b, c);
	return (b-a)/c + 1;
}