Möbius

For any positive integer $n$, the Möbius function $\mu(n)$ is defined. Its value is in $\{-1, 0, 1\}$, depending on the prime factorization of $n$.

• If $x$ is a square-free positive integer with an even number of prime factors, then $\mu(x) = 1$.
• If $x$ is a square-free positive integer with an odd number of prime factors, then $\mu(x) = -1$.
• If $x$ is divisible by the square of some prime, then $\mu(x) = 0$.

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

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

Let $k_y$ be the number of pairs $(i, j)$ with $1 \le i \le n$ and $1 \le j \le m$ such that $\mu(a_i \cdot b_j) = y$.

Compute $k_{-1}$, $k_{0}$, and $k_{1}$.

The first line contains two integers $n$ and $m$ ($1 \le n, m \le 2 \cdot 10^5$), 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.

Print three integers $k_{-1}$, $k_{0}$, and $k_{1}$ separated by spaces on a single line.