Tree

We generate two rooted trees with $n$ vertices as follows.

The first tree is generated as follows:

1. Vertex $1$ is the root of the tree.
2. For every $i \in [2,n]$, choose one vertex from $[1,i-1]$ as the parent of $i$.

The second tree is generated as follows:

1. Vertex $n$ is the root of the tree.
2. For every $i \in [1,n-1]$, choose one vertex from $[i+1,n]$ as the parent of $i$.

A way of generating the trees is good if and only if every vertex $i$ that is a leaf in tree 1 is not a leaf in tree 2, and every vertex $i$ that is not a leaf in tree 1 is a leaf in tree 2. The root of each tree is not a leaf, regardless of the number of adjacent edges.

For every $n \in [2,N]$, calculate the number of good ways to generate the trees. Two ways are different if and only if there is a vertex $i$ such that the parent of $i$ is different in at least one of the two trees. Output the answer modulo $M$.

The first line of input contains two integers $N$ and $M$ ($2 \le N \le 500$, $10 \le M \le 2^{30}$).

Output $N-1$ lines: the answers for $n=2,3,\ldots,N$.