Triple Jump#1579
The triple jump is performed as follows: the athlete accelerates, runs to a certain mark, and then makes three consecutive jumps. The winner is the one with the greatest total length of jumps.
You are participating in the competition and are the last to jump. All your opponents have already jumped, so their results are known.
You have already made your first jump, whose length is . The lengths of each of your remaining two jumps can independently take any real value from the interval [\textbf{lower},\ \textbf{upper}], with all values equally likely (not necessarily integers). You need to compute the probability that you will take the -th place. Your place number is equal to one plus the number of opponents who had longer triple jumps than you.
The input consists of several tests. The first line of each test contains the values , , (1 \leq \textbf{lower} \leq 1000, \textbf{lower} \leq \textbf{upper} \leq 1000, \textbf{lower} \leq \textbf{first} \leq \textbf{upper}), and the number of your opponents (1 \leq \textbf{n} \leq 50). The second line of each test contains integers from to — the lengths of your opponents' triple jumps.
For each test, print in a separate line exactly \textbf{n}+1 real numbers: the probabilities of you taking the first, second, ..., and last place, respectively. Print all probabilities with decimal digits.
Example 1