There are $N$ players playing a guessing game. Each player guesses a sequence consists of $\{1, 2, 3, 4, 5, 6\}$ with length $L$, then a dice will be rolled again and again and the roll out sequence will be recorded. The player whose guessing sequence first matches the last $L$ rolls of the dice wins the game.
Input
The first line is the number of test cases. For each test case, the first line contains 2 integers $N$ ($1 \le N \le 10$) and $L$ ($1 \le L \le 10$). Each of the following $N$ lines contains a guessing sequence with length $L$. It is guaranteed that the guessing sequences are consists of $\{1, 2, 3, 4, 5, 6\}$ and all the guessing sequences are distinct.
Output
For each test case, output a line containing the winning probability of each player with the precision of 6 digits.
Sample Input
3 5 1 1 2 3 4 5 6 2 1 1 2 1 3 1 4 1 5 1 6 1 4 3 1 2 3 2 3 4 3 4 5 4 5 6
Sample Output
0.200000 0.200000 0.200000 0.200000 0.200000 0.027778 0.194444 0.194444 0.194444 0.194444 0.194444 0.285337 0.237781 0.237781 0.239102