write a go solution for Description:
You are given a tree with n nodes. As a reminder, a tree is a connected undirected graph without cycles.

Let a_1,a_2,ldots,a_n be a sequence of integers. Perform the following operation exactly n times:

- Select an unerased node u. Assign a_u:= number of unerased nodes adjacent to u. Then, erase the node u along with all edges that have it as an endpoint.

For each integer k from 1 to n, find the number, modulo 998,244,353, of different sequences a_1,a_2,ldots,a_n that satisfy the following conditions:

- it is possible to obtain a by performing the aforementioned operations exactly n times in some order.
- operatornamegcd(a_1,a_2,ldots,a_n)=k. Here, operatornamegcd means the greatest common divisor of the elements in a.

Input Format:
The first line contains a single integer t (1<=t<=10,000)  — the number of test cases.

The first line of each test case contains a single integer n (2<=n<=10^5).

Each of the next n-1 lines contains two integers u and v (1<=u,v<=n) indicating there is an edge between vertices u and v. It is guaranteed that the given edges form a tree.

It is guaranteed that the sum of n over all test cases doesn't exceed 3*10^5.

Output Format:
For each test case, print n integers in a single line, where for each k from 1 to n, the k-th integer denotes the answer when operatornamegcd equals to k.

Note:
In the first test case,

- If we delete the nodes in order 1arrow2arrow3 or 1arrow3arrow2, then the obtained sequence will be a=[2,0,0] which has operatornamegcd equals to 2.
- If we delete the nodes in order 2arrow1arrow3, then the obtained sequence will be a=[1,1,0] which has operatornamegcd equals to 1.
- If we delete the nodes in order 3arrow1arrow2, then the obtained sequence will be a=[1,0,1] which has operatornamegcd equals to 1.
- If we delete the nodes in order 2arrow3arrow1 or 3arrow2arrow1, then the obtained sequence will be a=[0,1,1] which has operatornamegcd equals to 1.

Note that here we are counting the number of different sequences, not the number of different orders of deleting nodes.. Output only the code with no comments, explanation, or additional text.