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.

给你一棵树（即一个无环的无向连通图）和一个整数 $s$。

万尼亚希望为树的所有边赋予权重，使得所有权重均为非负实数，且它们的总和为 $s$。同时，他希望使该树的直径尽可能小。

我们定义加权树的直径为：树中任意两个顶点之间路径上所有边的权重之和的最大值。换言之，加权树的直径即树中最长简单路径的长度，其中路径的长度等于该路径上所有边的权重之和。

求万尼亚所能得到的最小可能直径。

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.

第一行包含两个整数 $n$ 和 $s$（$2 \leq n \leq 10^5$，$1 \leq s \leq 10^9$）—— 分别表示树中顶点的数量以及所有边权值的总和。

接下来的 $n-1$ 行，每行包含两个以空格分隔的整数 $a_i$ 和 $b_i$（$1 \leq a_i, b_i \leq n$，$a_i \neq b_i$）—— 表示由一条边连接的两个顶点的编号。这些边是无向的。

保证所给的边构成一棵树。

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 $\frac {|a-b|} {max(1, b)} \leq 10^{-6}$.

输出Vanya通过在树的边上赋予若干非负实数权重（权重总和为 $s$）所能得到的树的最小直径。

若你的答案的绝对误差或相对误差不超过 $10^{-6}$，则视为正确。

形式化地，设你的答案为 $a$，评测机的答案为 $b$。当且仅当 $\frac{|a-b|}{\max(1, b)} \leq 10^{-6}$ 时，你的答案被视为正确。

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:

在第一个例子中，需要按如下方式放置权重：

容易看出，该树的直径为 $2$。可以证明这是可能的最小直径。

在第二个例子中，需要按如下方式放置权重：