一棵树 - 题目

#7961. 一棵树

统计

题目描述

这里有一棵树，具体的，这是一张有 $n$ 个节点和 $n-1$ 条边组成的无向联通图。

每个节点初始颜色为白色，你需要恰好将其中 $k$ 个节点染成黑色，定义一条边的权值是，断开这条边之后，两个连通块的黑色节点个数之差，定义一棵树的权值为所有边的权值求和，你需要最小化整棵树的权值。

输入格式

第一行两个正整数 $n,k$（$1\leq k\leq n\leq 5\times10^5$）。

接下来 $n-1$ 行，每行两个正整数 $x,y$ 表示树上的一条边。

输出格式

输出共 $1$ 行，表示最优的染色方案下，这棵树的权值的最小值。

样例1输入

样例1输出

样例1解释

下图展示了一种满足条件的染色方案，边上的数字表示边权。

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