Appropriate Team

2000ms

262144K

Description:

Since next season are coming, you'd like to form a team from two or three participants. There are $$$n$$$ candidates, the $$$i$$$-th candidate has rank $$$a_i$$$. But you have weird requirements for your teammates: if you have rank $$$v$$$ and have chosen the $$$i$$$-th and $$$j$$$-th candidate, then $$$GCD(v, a_i) = X$$$ and $$$LCM(v, a_j) = Y$$$ must be met.

You are very experienced, so you can change your rank to any non-negative integer but $$$X$$$ and $$$Y$$$ are tied with your birthdate, so they are fixed.

Now you want to know, how many are there pairs $$$(i, j)$$$ such that there exists an integer $$$v$$$ meeting the following constraints: $$$GCD(v, a_i) = X$$$ and $$$LCM(v, a_j) = Y$$$. It's possible that $$$i = j$$$ and you form a team of two.

$$$GCD$$$ is the greatest common divisor of two number, $$$LCM$$$ — the least common multiple.

Input:

First line contains three integers $$$n$$$, $$$X$$$ and $$$Y$$$ ($$$1 \le n \le 2 \cdot 10^5$$$, $$$1 \le X \le Y \le 10^{18}$$$) — the number of candidates and corresponding constants.

Second line contains $$$n$$$ space separated integers $$$a_1, a_2, \dots, a_n$$$ ($$$1 \le a_i \le 10^{18}$$$) — ranks of candidates.

Output:

Print the only integer — the number of pairs $$$(i, j)$$$ such that there exists an integer $$$v$$$ meeting the following constraints: $$$GCD(v, a_i) = X$$$ and $$$LCM(v, a_j) = Y$$$. It's possible that $$$i = j$$$.

Sample Input:

12 2 2
1 2 3 4 5 6 7 8 9 10 11 12

Sample Output:

Sample Input:

12 1 6
1 3 5 7 9 11 12 10 8 6 4 2

Sample Output:

Note:

In the first example next pairs are valid: $$$a_j = 1$$$ and $$$a_i = [2, 4, 6, 8, 10, 12]$$$ or $$$a_j = 2$$$ and $$$a_i = [2, 4, 6, 8, 10, 12]$$$. The $$$v$$$ in both cases can be equal to $$$2$$$.

In the second example next pairs are valid:

$$$a_j = 1$$$ and $$$a_i = [1, 5, 7, 11]$$$;
$$$a_j = 2$$$ and $$$a_i = [1, 5, 7, 11, 10, 8, 4, 2]$$$;
$$$a_j = 3$$$ and $$$a_i = [1, 3, 5, 7, 9, 11]$$$;
$$$a_j = 6$$$ and $$$a_i = [1, 3, 5, 7, 9, 11, 12, 10, 8, 6, 4, 2]$$$.

Informação

Provedor Codeforces

Código CF1016G