P17207 "DLESS-6" Melting

> Now, even if I "melt" you, who was floating in the sky, into the air, > there is still a feeling that will not change.

You are given a positive integer $n$ and five sets $A, B, C, D, E$ consisting of integers in $[0, 2^n)$. For two non-negative integers $x, i$, define $x_i = \lfloor x / 2^i \rfloor \bmod 2$, i.e., the $(i+1)$-th bit of $x$ in binary from low to high. For a set $S$ consisting of non-negative integers, define a 5-tuple $(a, b, c, d, e)$ to be fair for $S$ if and only if: - $a \in A$, $b \in B$, $c \in C$, $d \in D$, $e \in E$; - For every $i \in S$, in $[a_i, b_i, c_i, d_i, e_i]$, the counts of $0$ and $1$ differ by at most $1$. For all $S \subseteq \{0, 1, \cdots, n-1\}$, compute the number of 5-tuples that are fair for $S$. Output the answer modulo the given positive integer $P$.

The first line contains two positive integers $n, P$, representing the value range of the numbers and the modulus for the answers. The next five lines each describe a set using $2^n$ characters from `01`. If the $i$-th character is `1`, then $i - 1$ is in the set; otherwise, $i - 1$ is not in the set. The five sets described are $A, B, C, D, E$, respectively.

Output $2^n$ lines, each containing one non-negative integer. Line $k$ gives the answer for the set $S = \{ i \mid (k - 1)_i = 1 \}$.

**[Sample #1 Explanation]** For $S = \{0, 1\}$, the three 5-tuples that are fair for $S$ are: $(0, 2, 1, 0, 3)$, $(0, 2, 3, 0, 1)$, $(0, 2, 3, 0, 3)$. **[Constraints]** For all testdata, $1 \le n \le 15$, $10^8 \le P \le 10^9$. **This problem uses bundled testcases**. There are $10$ subtasks, each worth $10$ points. Subtask $i$ satisfies $n = i + 5$. Translated by ChatGPT 5