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: