For a tree (T) with (n \ge 2) vertices, consider the standard process for generating its Prufer sequence . We repeatedly perform the following steps until only two vertices remain: Select the leaf with the smallest label; Remove it from the tree. It is known that vertex (n) is always one of the two remaining vertices. Let (v) be the other remaining vertex. We define the Prufer vertex of (T) as (P(T) = v). You are given a forest with (n) vertices and (m) edges. Let (k) be the number of connected components in this forest, and let their sizes be (s_1, s_2, \ldots, s_k). It is known that there are exactly (n^{k - 2} \prod\limits_{i=1}^k s_i) ways to add edges to the forest so that it becomes a single tree. For each (v) ((1 \le v < n)), calculate how many of these ways result in a tree (T) satisfying (P(T) = v). Since the answers can be large, print them modulo (998\,244\,353). Each test contains multiple test cases. The first line contains the number of test cases (t) ((1 \le t \le 10^4)). The description of the test cases follows. The first line of each test case contains two integers (n) and (m) ((2 \le n \le 2 \cdot 10^5), (0 \le m \le n - 1)) — the number of vertices and edges in the forest, respectively. The next (m) lines of each test case contain two integers (u) and (v) ((1 \le u, v \le n, u \neq v)), describing an edge between vertices (u) and (v). It is guaranteed that these edges form a forest (that is, the graph is acyclic). It is guaranteed that the sum of (n) over all test cases does not exceed (2 \cdot 10^5). For each test case, print (n - 1) integers on a single line. The (i)-th integer should be the number of ways to add edges to the forest so that it becomes a tree (T) satisfying (P(T) = i), modulo (998\,244\,353). In the first example, there are no edges in the forest, and there are (3) ways to comp