Guessing the Dice Roll

Time Limit: 2000/1000 MS (Java/Others)

Memory Limit: 65536/65536 K (Java/Others)

Description

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 ≤ N ≤ 10) and L (1 ≤ L ≤ 10). Each of the following N lines contains a guessing sequence with length L. It is guaranteed that the guessing sequences are consist 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

Hint

jiangzijing2015

Source

2016ACM/ICPC亚洲区沈阳站-重现赛(感谢东北大学)

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