Möbius

For any positive integer $n$, let's define Möbius function $\mu(n)$. It has values in $\\{-1, 0, 1\\}$ depending on the factorization of $n$ into prime factors:

• $\mu(x) = 1$ if $x$ is a square-free positive integer with an even number of prime factors.
• $\mu(x) = -1$ if $x$ is a square-free positive integer with an odd number of prime factors.
• $\mu(x) = 0$ if $x$ has is divisible by some squared prime factor.

For example, $\mu(1) = 1, \mu(2) = -1, \mu(6) = 1, \mu(12) = 0$.

You are given two arrays $a$ and $b$, consisting of positive integers.

Let $k\_y$ be the number of pairs $(i, j), 1 \le i \le n, 1 \le j \le m$ such that $\mu(a\_i\cdot b\_j)$ is equal to $y$.

Your task is to calculate $k\_{-1}$, $k\_{0}$ and $k\_1$.

The first line of input contains two integers $n, m$ ($1 \le n, m \le 2 \cdot 10^5$) --- the sizes of arrays $a$ and $b$.

The second line contains $n$ integers $a\_i$ ($1 \le a\_i \le 10^6$) separated by spaces.

The third line contains $m$ integers $b\_i$ ($1 \le b\_i \le 10^6$) separated by spaces.

Output three integers $k\_{-1}, k\_{0}, k\_{1}$ separated by spaces in a single line, where $k\_y = |\\{(i, j) : \mu(a\_i \cdot b\_j) = y \\}|$.