write a go solution for Description:
Kawashiro Nitori is a girl who loves competitive programming. One day she found a rooted tree consisting of n vertices. The root is vertex 1. As an advanced problem setter, she quickly thought of a problem.

Kawashiro Nitori has a vertex set U=1,2,ldots,n. She's going to play a game with the tree and the set. In each operation, she will choose a vertex set T, where T is a partial virtual tree of U, and change U into T.

A vertex set S_1 is a partial virtual tree of a vertex set S_2, if S_1 is a subset of S_2, S_1neqS_2, and for all pairs of vertices i and j in S_1, operatornameLCA(i,j) is in S_1, where operatornameLCA(x,y) denotes the lowest common ancestor of vertices x and y on the tree. Note that a vertex set can have many different partial virtual trees.

Kawashiro Nitori wants to know for each possible k, if she performs the operation exactly k times, in how many ways she can make U=1 in the end? Two ways are considered different if there exists an integer z (1<=z<=k) such that after z operations the sets U are different.

Since the answer could be very large, you need to find it modulo p. It's guaranteed that p is a prime number.

Input Format:
The first line contains two integers n and p (2<=n<=2000, 10^8+7<=p<=10^9+9). It's guaranteed that p is a prime number.

Each of the next n-1 lines contains two integers u_i, v_i (1<=u_i,v_i<=n), representing an edge between u_i and v_i.

It is guaranteed that the given edges form a tree.

Output Format:
The only line contains n-1 integers — the answer modulo p for k=1,2,ldots,n-1.

Note:
In the first test case, when k=1, the only possible way is:

1. 1,2,3,4to1.

When k=2, there are 6 possible ways:

1. 1,2,3,4to1,2to1;
2. 1,2,3,4to1,2,3to1;
3. 1,2,3,4to1,2,4to1;
4. 1,2,3,4to1,3to1;
5. 1,2,3,4to1,3,4to1;
6. 1,2,3,4to1,4to1.

When k=3, there are 6 possible ways:

1. 1,2,3,4to1,2,3to1,2to1;
2. 1,2,3,4to1,2,3to1,3to1;
3. 1,2,3,4to1,2,4to1,2to1;
4. 1,2,3,4to1,2,4to1,4to1;
5. 1,2,3,4to1,3,4to1,3to1;
6. 1,2,3,4to1,3,4to1,4to1.. Output only the code with no comments, explanation, or additional text.