Post's Correspondence Problem

문제

Let $AA$ and $BB$ be two sequences of non-empty strings:

Let $mm$ be a positive integer. Does there exist a sequence of integers $i_1,i_2,\dots ,i_{k}i\_1,\; i\_2,\; \backslash dots,\; i\_k$ such that $m>k>0m\; >\; k\; >\; 0$ and $a_{i_1}{a}_{i_2}\dots a_{i_k}=b_{i_1}{b}_{i_2}\dots b_{i_k}a\_\{i\_1\}\; a\_\{i\_2\}\; \backslash dots\; a\_\{i\_k\}\; =\; b\_\{i\_1\}\; b\_\{i\_2\}\; \backslash dots\; b\_\{i\_k\}$?

For example, if $A=(a,abaaa,ab)A\; =\; (a,\; abaaa,\; ab)$ and $B=(aaa,ab,b)B\; =\; (aaa,\; ab,\; b)$, then the required sequence of integers is $(2,1,1,3)(2,\; 1,\; 1,\; 3)$ giving $abaaaaaab=abaaaaaababaaaaaab\; =\; abaaaaaab$.

입력

The first two lines of input will contain $mm$ and $nn$ respectively, and $m\times n\le 40m\; \backslash times\; n\; \backslash le\; 40$. The next $2n2n$ lines contain in order the elements of $AA$ followed by the elements of $BB$. Each string is at most $2020$ characters.

출력

If a solution exists, print $kk$ on a line by itself, followed by the integer sequence in order, one element per line. Otherwise, print a single line containing No solution..