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.</p>

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.

입력 형식

On the first line an integer t (1 ≤ t ≤ 100): the number of test cases. Then for each test case:</p>

• 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).

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.

예제 입력

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

예제 출력

ale alt apt opt

힌트

If s and t are strings of equal length and s_i denotes the ith 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.