E. Youtime limit per test5 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou 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.  \operatorname{gcd}(a_1, a_2, \ldots, a_n) = k. Here, \operatorname{gcd} means the greatest common divisor of the elements in a. InputThe first line contains a single integer t (1 \le t \le 10\,000)  — the number of test cases.The first line of each test case contains a single integer n (2 \le n \le 10^5).Each of the next n - 1 lines contains two integers u and v (1 \le u, v \le 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 \cdot 10^5.OutputFor 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 \operatorname{gcd} equals to k.ExampleInput
2
3
2 1
1 3
2
1 2
Output
3 1 0
2 0
NoteIn the first test case,     If we delete the nodes in order 1 \rightarrow 2 \rightarrow 3 or 1 \rightarrow 3 \rightarrow 2, then the obtained sequence will be a = [2, 0, 0] which has \operatorname{gcd} equals to 2.  If we delete the nodes in order 2 \rightarrow 1 \rightarrow 3, then the obtained sequence will be a = [1, 1, 0] which has \operatorname{gcd} equals to 1.  If we delete the nodes in order 3 \rightarrow 1 \rightarrow 2, then the obtained sequence will be a = [1, 0, 1] which has \operatorname{gcd} equals to 1.  If we delete the nodes in order 2 \rightarrow 3 \rightarrow 1 or 3 \rightarrow 2 \rightarrow 1, then the obtained sequence will be a = [0, 1, 1] which has \operatorname{gcd} equals to 1. Note that here we are counting the number of different sequences, not the number of different orders of deleting nodes.
2
3
2 1
1 3
2
1 2

3 1 0 2 0 
['dfs and similar', 'dp', 'math', 'number theory', '*2600']