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Тренировка 5

A. Word Ladder B. Bonus Word C. Contest D. Cycling E. Escape F. Settling Salesman Problem G. Space H. Herbert

A. Word Ladder

Ограничения: время – 2s/4s, память – 64MiB Ввод: input.txt или стандартный ввод Вывод: output.txt или стандартный вывод copy
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A word ladder is a sequence of words, in which two consecutive words differ by exactly one letter. An example of such a ladder (usually arranged vertically, hence the "ladder") would be: beer, brew, brow, word, down. Note that to get from one word to the next, the letters may be rearranged, and exactly one letter is changed.

For this problem, you will be given a dictionary of distinct words, all of the same length. Your task is to write a program that finds a word ladder of minimal length, such that the first and last word of the ladder have no letters in common.

Input

On the first line an integer `t` (`1\ ≤\ t\ ≤\ 100`): the number of test cases. Then for each test case:

A line with two space-separated integers `n` (`2\ ≤\ n\ ≤\ 100`) and `l` (`1\ ≤\ l\ ≤\ 20`): the number of words and their length.
`n` lines with a word, each consisting of `l` lowercase letters (a – z).

Output

For each testcase:

a single line with the words in a ladder of minimal length, separated by a single space.

It is guaranteed that at least one such ladder can be constructed. If there is more than one, output the one that comes first lexicographically.

Notes

If `s` and `t` are strings of equal length and `s_i` denotes the `i`th character of `s`, then `s` precedes `t` lexicographically if for some `i`: `s_i\ <\ t_i` and `s_j` = `t_j` for all `j\ <\ i`.

Sample input

1
9 3
alt
spy
sea
opt
pea
ape
spa
apt
ale

Sample output

ale alt apt opt

Source: BAPC preliminary contest, 2007