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

First, choose $n$ distinct integers between $1$ and $m$, inclusive.

Sort these numbers in nondecreasing order.

Take the difference sequence, which transforms a sequence $a_1$, $a_2$, $a_3$, $\ldots $ into $a_1$, $a_2a_1$, $a_3a_2$, $\ldots $

Sort the difference sequence in nondecreasing order.

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 $m = 10$:

Suppose we initially chose $6$, $2$, $9$.

The sequence in order is $2$, $6$, $9$.

The difference sequence is $2$, $4$, $3$.

The sorted difference sequence is $2$, $3$, $4$.

The prefix sums of the sorted difference sequence are $2$, $5$, $9$.
Suppose you chose a uniformly random set of distinct integers for step $1$. Compute the expected value for each index in the final sequence.
Input
The single line of input contains two integers $n$ ($1 \le n \le 50$) and $m$ ($n \le m \le 10\, 000$), where $n$ is the size of the sequence, and all of the initial integers chosen are in the range from $1$ to $m$.
Output
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 $10^{6}$.
Sample Input 1  Sample Output 1 

3 5 
1 2.3 4.5 