Before the game begins, each of n students writes down a unique string of length m consisting of only ‘H’ for head and ‘T’ for tail (any 2 students will not write the same string). Subsequently, when the game begins, a fair coin is flipped repeatedly until the last m flips matches one of the pre-written strings. Compute the probability of each student winning a prize. Input A number of of inputs (≤ 100) with the following format. The first line has n, m. Next, we have n lines, each with a string of length m consisting of ‘H’ and ‘T’. Note that 1 ≤ n, m ≤ 300. Output Print the probability of each student winning, one on each line. Round to 6 digits after decimal. Sample Input 33 THT TTH HTT Sample Output 0.333333 0.250000 0.416667