题目描述

The cows have set up a telephone network, which for the purposes of this problem can be considered to be an unrooted tree of unspecified degree with N (1 <= N <= 100,000) vertices conveniently numbered 1..N. Each vertex represents a telephone switchboard, and each edge represents a telephone wire between two switchboards. Edge i is specified by two integers A_i and B_i the are the two vertices joined by edge i (1 <= A_i <= N; 1 <= B_i <= N; A_i != B_i).

Some switchboards have only one telephone wire connecting them to another switchboard; these are the leaves of the tree, each of which is a telephone booth located in a cow field.

For two cows to communicate, their conversation passes along the unique shortest path between the two vertices where the cows are located. A switchboard can accomodate only up to K (1 <= K <= 10) simultaneous conversations, and there can be at most one conversation going through a given wire at any one time.

Given that there is a cow at each leaf of the tree, what is the maximum number of pairs of cows that can simultaneously hold

conversations? A cow can, of course, participate in at most one conversation.

1   5          C1   C5 
|   |          ||   || 
2---4   -->    |2---4| 
|   |          ||   || 
3   6          C3   C6 

Consider this six-node telephone tree with K=1:

There are four cows, located at vertices 1, 3, 5 and 6. If cow 1 talks to cow 3, and cow 5 talks to cow 6, then they do not exceed the maximum number of conversations per switchboard, so for this example the answer is 2 (for two pairs of cows talking simultaneously).

奶牛们要建立一个电话网络，它们可以被认为是一个无根树（大概是个图吧。。。），里面N (1 <= N <= 100,000)个结点可以简便的编号为1...N。每一个结点代表一个电话交换机（类似开关），每条边代表一个连接两个电话交换机的电话线。边i是用两个整数A_i和B_i表示的，也就是该边连接着A_i和B_i两个电话交换机(1 <= A_i <= N; 1 <= B_i <= N; A_i != B_i).

一些电话交换机只有一根电话线；它们是这棵树的叶子结点，每个叶子结点只有一只牛。当两头牛在通话时，它们的对话沿着唯一的在两头牛所在结点的最短路径。

一个电话交换机只能忙于K(1 <= K <= 10)个同时的对话，而且每个电话线同一时间只能传送一个对话。

给出一个每个叶子结点都有一头牛的树， 问最多有多少对奶牛能在同一时间进行它们的对话？

输入格式

* Line 1: Two space separated integers: N and K

* Lines 2..N: Line i+1 contains two space-separated integers: A_i and B_i

输出格式

* Line 1: The number of pairs of cows that can simultaneously hold conversations

6 1 
1 2 
2 3 
2 4 
4 5 
4 6 

2