25228번 - Double Sort 스페셜 저지다국어

문제

Given two integers $n$ and $m$ ($n \le m$), you generate a sequence of $n$ integers as follows:

1. First, choose $n$ distinct integers between 1ドル$ and $m,ドル inclusive.
2. Sort these numbers in non-decreasing order.
3. Take the difference sequence, which transforms a sequence $a_1,ドル $a_2,ドル $a_3,ドル $\ldots$ into $a_1,ドル $a_2-a_1,ドル $a_3-a_2,ドル $\ldots$
4. Sort the difference sequence in non-decreasing order.
5. Take the prefix sums of the sorted difference sequence to get the final sequence. This transforms a sequence $b_1,ドル $b_2,ドル $b_3,ドル $\ldots$ into $b_1,ドル $b_2+b_1,ドル $b_3+b_2+b_1,ドル $\ldots$

For example, with $n = 3$ and $m = 10$:

1. Suppose we initially chose 6ドル,ドル 2ドル,ドル 9ドル$.
2. The sequence in order is 2ドル,ドル 6ドル,ドル 9ドル$.
3. The difference sequence is 2ドル,ドル 4ドル,ドル 3ドル$.
4. The sorted difference sequence is 2ドル,ドル 3ドル,ドル 4ドル$.
5. The prefix sums of the sorted difference sequence are 2ドル,ドル 5ドル,ドル 9ドル$.

Suppose you chose a uniformly random set of distinct integers for step 1ドル$. Compute the expected value for each index in the final sequence.

입력

The single line of input contains two integers $n$ (1ドル \le n \le 50$) and $m$ ($n \le m \le 10,000円$), where $n$ is the size of the sequence, and all of the initial integers chosen are in the range from 1ドル$ to $m$.

출력

Output $n$ lines. Each line contains a single real number, which is the expected value at that index of the final sequence. Each answer is accepted with absolute or relative error at most 10ドル^{-6}$.

제한

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