CF1085D Minimum Diameter Tree

You are given a tree (an undirected connected graph without cycles) and an integer $ s $ . Vanya wants to put weights on all edges of the tree so that all weights are non-negative real numbers and their sum is $ s $ . At the same time, he wants to make the diameter of the tree as small as possible. Let's define the diameter of a weighed tree as the maximum sum of the weights of the edges lying on the path between two some vertices of the tree. In other words, the diameter of a weighed tree is the length of the longest simple path in the tree, where length of a path is equal to the sum of weights over all edges in the path. Find the minimum possible diameter that Vanya can get.

The first line contains two integer numbers $ n $ and $ s $ ( $ 2 \leq n \leq 10^5 $ , $ 1 \leq s \leq 10^9 $ ) — the number of vertices in the tree and the sum of edge weights. Each of the following $ n−1 $ lines contains two space-separated integer numbers $ a_i $ and $ b_i $ ( $ 1 \leq a_i, b_i \leq n $ , $ a_i \neq b_i $ ) — the indexes of vertices connected by an edge. The edges are undirected. It is guaranteed that the given edges form a tree.

Print the minimum diameter of the tree that Vanya can get by placing some non-negative real weights on its edges with the sum equal to $ s $ . Your answer will be considered correct if its absolute or relative error does not exceed $ 10^{-6} $ . Formally, let your answer be $ a $ , and the jury's answer be $ b $ . Your answer is considered correct if $ \frac {|a-b|} {max(1, b)} \leq 10^{-6} $ .

In the first example it is necessary to put weights like this: It is easy to see that the diameter of this tree is $ 2 $ . It can be proved that it is the minimum possible diameter. In the second example it is necessary to put weights like this: