B"This version of the problem differs from the previous one only in the constraint on n . A tree is a connected undirected graph without cycles. A weighted tree has a weight assigned to each edge. The distance between two vertices is the minimum sum of weights on the path connecting them. You are given a weighted tree with n vertices, each edge has a weight of 1 . Denote d(v) as the distance between vertex 1 and vertex v . Let f(x) be the minimum possible value of max limits_{1 <= q v <= q n} {d(v)} if you can temporarily add an edge with weight x between any two vertices a and b (1 <= a, b <= n) . Note that after this operation, the graph is no longer a tree. For each integer x from 1 to n , find f(x) . The first line contains a single integer t ( 1 <= t <= 10^4 ) -- the number of test cases. The first line of each test case contains a single integer n ( 2 <= n <= 3 cdot 10^5 ). Each of the next n xe2 x88 x921 lines contains two integers u and v ( 1 <= u,v <= n ) indicating that 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 . For each test case, print n integers in a single line, x -th of which is equal to f(x) for all x from 1 to n . "...