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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <iostream>
#include <string>
#include <vector>
#include <algorithm>
#include <numeric>
using namespace std;

long long int lcm(long long int A, long long int B);
long long int gcd(long long int A, long long int B);

int main(void) {

	// TODO: submit前にprintf-debugの削除確認！
	long long int A, B, C, D;
	cin >> A >> B >> C >> D;

	long long int cnt = B - A + 1;
	long long int divCCnt = (B/C) - ((A-1)/C);
	long long int divDCnt = (B/D) - ((A-1)/D);
	long long int divCDCnt = (B/lcm(C, D)) - ((A-1)/lcm(C, D));

	long long int ans = cnt - (divCCnt + divDCnt - divCDCnt);
	
	cout << ans;
	return 0;
}

long long int lcm(long long int A, long long int B) {
	return (A*B)/gcd(A, B);

}

long long int gcd(long long int A, long long int B) {
	long long int l, s;
	if(A > B) {
		l = A;
		s = B;
	} else {
		l = B;
		s = A;
	}

	while(l % s != 0) {
		long long int newS = l % s;
		l = s;
		s = newS;
	}
	return s;

}