A prime $p$, and polynomials in $K$ variables over $\mathbb{Z}/p\mathbb{Z}$, $f(x_1, x_2, ..., x_K)$ and $g(x_1, x_2, ..., x_K)$ are given.
Calculate a product of $f$ and $g$ with $\bmod (1-x_1^{N_1}, 1-x_2^{N_2}, ..., 1-x_K^{N_K})$.
Here, $N_i$ is a divisor of $p-1$. 

$P$ $K$
$N_1$ $N_2$ ... $N_K$
$f$
$g$
$f$, $g$ is the integer array of length $\prod N_i$ consisting of integers between $0$ and $p-1$.
$i = i_1 + i_2 N_1 + ... + i_K N_1 N_2 ... N_{K-1}$-th element is corresponded to the coefficient of the $(x_1^{i_1}, x_2^{i_2}, ..., x_K^{i_K})$.

$fg$
$fg$ is the integer array of length $\prod N_i$ consisting of integers between $0$ and $p-1$. 
As the same with input format, $i = i_1 + i_2 N_1 + ... + i_K N_1 N_2 ... N_{K-1}$-th element is corresponded to the coefficient of the $(x_1^{i_1}, x_2^{i_2}, ..., x_K^{i_K})$.

- $2 \leq p \leq 10^9$
- $p$ is a prime
- $0 \leq K \leq 18$
- $\prod N_i \leq 2^{18}$
- $2 \leq N_i$
- $N_i$ is a divisor of $p-1$