Double Sort

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

1. Choose $n$ distinct integers between $1$ and $m$, inclusive.
2. Sort these numbers in non-decreasing order.
3. Take the difference sequence, which transforms a sequence $a_1, a_2, a_3, \ldots$ into $a_1, a_2-a_1, a_3-a_2, \ldots$.
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 $b_1, b_2, b_3, \ldots$ into $b_1, b_2+b_1, b_3+b_2+b_1, \ldots$.

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

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

Suppose the set of distinct integers in step 1 is chosen uniformly at random. Compute the expected value at each position of the final sequence.

The input consists of a single line containing two integers $n$ and $m$ ($1 \le n \le 50$, $n \le m \le 10\,000$). Here $n$ is the sequence length, and the initial integers are chosen from $1$ to $m$ inclusive.

Output $n$ lines. Each line contains one real number, the expected value at the corresponding position of the final sequence. An answer is accepted if its absolute or relative error is at most $10^{-6}$.