example of a chainword is the accompanying triple: a line of m lowercase Latin letters; the main clue: an arrangement of fragments with the end goal that the letters that compare to each portion spell a word from the word reference; the subsequent clue: one more succession of portions with the end goal that the letters that relate
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example of a chainword is the accompanying triple:
a line of m lowercase Latin letters;
the main clue: an arrangement of fragments with the end goal that the letters that compare to each portion spell a word from the word reference;
the subsequent clue: one more succession of portions with the end goal that the letters that relate to each section spell a word from the word reference.
Note that the successions of portions don't really need to be unmistakable.
Two occasions of chainwords are considered unique on the off chance that they have various strings, diverse first clues or distinctive second clues.
Count the number of various examples of chainwords. Since the number may be really huge, output it modulo 998244353.
Input
The primary line contains two integers n and m (1≤n≤8, 1≤m≤109) — the number of words in the word reference and the number of letter cells.
Every one of the following n lines contains a word — a non-void line of close to 5 lowercase Latin letters. All words are pairwise unmistakable.
Output
Print a solitary integer — the number of various occasions of chainwords of length m for the given word reference modulo 998244353.
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