At this point we already know that students love to sleep. Patrik is a
record holder in this category. He wakes up only when he needs to eat
or if he wishes to play FIFA 20. Therefore, his dreams usually revolve
around football. In his last dream, he found himself in the role of a football
manager of his favourite team – GNK Dinamo Zagreb.
His job is to select \(N\) players that will defend the blue colors in the next
season, but the board has some peculiar requests. They are:
• All players must have surnames of distinct lengths.
• Surname of a player must appear as a continuous subsequence of surnames of all players whose
surnames are longer.
To make his job easier, Patrik divided the potential players in \(N\) buckets such that players in \(i-th\) bucket
have exactly \(i\) letters in their surname. In each of these buckets there are exactly \(K\) players. Patrik wants
to know in how many distinct ways (modulo \(10^{9} + 7\)) can he choose the players for his squad while also
conforming to the given requests.

The first line contains two integers \(N\) (\(1 \le N \le 50\)) and \(K\) (\(1 \le K \le 1\,500\)).
Each of the next \(N\) lines contains \(K\) not necessarily distinct surnames of players. The surnames of players
in \(i-th\) of those lines consist of exactly \(i\) lowercase letters from the English alphabet.

In the only line you should output the answer from the task description.
Bodovanje
Subtask
Score
Constraints
1
22
\(N = 5\) and \(K = 10\)
2
33
\(N = 50\) and \(K = 100\)
3
55
No additional constraints.

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출처 COCI 2019/2020 Contest 6