Power Tree

题意翻译

给定一棵 $n$ 个点的有根树，$1$ 为根。定义 $u$ 为叶子当且仅当它**不是根**且度数为 $1$。 你可以选择花费 $w_u$ 的代价控制 $u$ 点。当一个点被控制时你可以选择给它的子树内的叶子的点权都加上一个值 $v$ 。你需要控制若干个点，使得花费的代价尽量少，无论怎样规定叶子的初始点权，都可以通过操作你选择的点来让所有叶子的点权清空。 **输出格式** 你需要输出代价和的最小值以及所有点，满足它存在于某一种最优选择中。 $n\le 2\times 10^5$

题目描述

You are given a rooted tree with $ n $ vertices, the root of the tree is the vertex $ 1 $ . Each vertex has some non-negative price. A leaf of the tree is a non-root vertex that has degree $ 1 $ . Arkady and Vasily play a strange game on the tree. The game consists of three stages. On the first stage Arkady buys some non-empty set of vertices of the tree. On the second stage Vasily puts some integers into all leaves of the tree. On the third stage Arkady can perform several (possibly none) operations of the following kind: choose some vertex $ v $ he bought on the first stage and some integer $ x $ , and then add $ x $ to all integers in the leaves in the subtree of $ v $ . The integer $ x $ can be positive, negative of zero. A leaf $ a $ is in the subtree of a vertex $ b $ if and only if the simple path between $ a $ and the root goes through $ b $ . Arkady's task is to make all integers in the leaves equal to zero. What is the minimum total cost $ s $ he has to pay on the first stage to guarantee his own win independently of the integers Vasily puts on the second stage? Also, we ask you to find all such vertices that there is an optimal (i.e. with cost $ s $ ) set of vertices containing this one such that Arkady can guarantee his own win buying this set on the first stage.

输入输出格式

输入格式

The first line contains a single integer $ n $ ( $ 2 \le n \le 200\,000 $ ) — the number of vertices in the tree. The second line contains $ n $ integers $ c_1, c_2, \ldots, c_n $ ( $ 0 \le c_i \le 10^9 $ ), where $ c_i $ is the price of the $ i $ -th vertex. Each of the next $ n - 1 $ lines contains two integers $ a $ and $ b $ ( $ 1 \le a, b \le n $ ), denoting an edge of the tree.

输出格式

In the first line print two integers: the minimum possible cost $ s $ Arkady has to pay to guarantee his own win, and the number of vertices $ k $ that belong to at least one optimal set. In the second line print $ k $ distinct integers in increasing order the indices of the vertices that belong to at least one optimal set.

输入输出样例

输入样例 #1

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

输出样例 #1

4 3
2 4 5 

输入样例 #2

3
1 1 1
1 2
1 3

输出样例 #2

2 3
1 2 3 

说明

In the second example all sets of two vertices are optimal. So, each vertex is in at least one optimal set.