Rikka with Subset II

As we know, Rikka is poor at math. Yuta is worrying about this situation, so he gives Rikka some math tasks to practice. There is one of them:

Yuta has a tree with n vertices, the length of each edge is exactly 1. For any none empty subset S of the vertices, value(S) is equal to max(dis(u,v))(u,v \in S) which dis(u,v) is equal to the distance between u and v on the tree.

It is easy to find that value(S) satisfy 0<=value(S)<n. Now For each K in [0,n), Yuta wants to know the number of the subset S which satisfy value(S)=K.

It is too difficult for Rikka. Can you help her?

The first line contains a number t(1<=t<=100), the number of the testcases. And there are no more than 5 testcases with n>100.

For each testcase, the first line contains a number n(1<=n<=3000). Then n-1 lines follow, each line contains two numbers u and v, which means there is an edge between u and v.

For each testcase, print a line contains exactly n numbers, the ith number is the number of none empty subsets S which satisfy value(S)=i-1. The answer may be very large, so you only need to print the answer module 998244353.

2
2
1 2
4
1 3
2 4
4 1

2 1
4 3 4 4

学军中学

2016 Multi-University Training Contest 8