B"You are given a rooted tree, consisting of n vertices, numbered from 1 to n . Vertex 1 is the root. Additionally, the root only has one child. You are asked to add exactly k edges to the tree (possibly, multiple edges and/or edges already existing in the tree). Recall that a bridge is such an edge that, after you remove it, the number of connected components in the graph increases. So, initially, all edges of the tree are bridges. After k edges are added, some original edges of the tree are still bridges and some are not anymore. You want to satisfy two conditions: Solve the task for all values of k from 1 to n - 1 and output the smallest number of bridges. The first line contains a single integer t ( 1 <= t <= 10^4 ) -- the number of testcases. The first line of each testcase contains a single integer n ( 2 <= n <= 3 cdot 10^5 ) -- the number of vertices of the tree. Each of the next n - 1 lines contain two integers v and u ( 1 <= v, u <= n ) -- the description of the edges of the tree. It's guaranteed that the given edges form a valid tree. Additional constraint on the input: the root (vertex 1 ) has exactly one child. The sum of n over all testcases doesn't exceed 3 cdot 10^5 . For each testcase, print n - 1 integers. For each k from 1 to n - 1 print the smallest number of bridges that can be left after you add k edges to the tree. "...