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F - typewriter

Score : $500$ points

Problem Statement

We have a typewriter with $N$ rows. The keys in the $i$-th row from the top can type the characters in a string $S_i$.

Let us use this keyboard to enter a string, as follows.

• First, choose an integer $1 \le k \le N$.
• Then, start with an empty string and only use the keys in the $k$-th row from the top to enter a string of length exactly $L$.

How many strings of length $L$ can be entered in this way? Since the answer can be enormous, print it modulo $998244353$.

Constraints

• $N$ and $L$ are integers.
• $1 \le N \le 18$
• $1 \le L \le 10^9$
• $S_i$ is a (not necessarily contiguous) non-empty subsequence of abcdefghijklmnopqrstuvwxyz.

Input

Input is given from Standard Input in the following format:

$N$ $L$

$S_1$

$S_2$

$\dots$

$S_N$

Output

Print the answer.

2 2
ab
ac

7

We can enter seven strings: aa, ab, ac, ba, bb, ca, cc.

4 3
abcdefg
hijklmnop
qrstuv
wxyz

1352

5 1000000000
abc
acde
cefg
abcfh
dghi

346462871

Be sure to print the answer modulo $998244353$.