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EIHTP - The highest total point

Given a rooted tree with each node has a “point” value. Find a path that has total points of all nodes in the path is highest.

Input

The first line contains two integer n and m which are the number of nodes in the tree and the root of the given tree. Nodes are numbered from 0 to n - 1 (0 ≤ m < n ≤ 105)

The second line contains n integers which are points of all nodes, respectively.

Each line in the next (n – 1) lines contains two integers a, b which represent an edge in the tree.

Output

An integer representing the highest total point.

Sample

Input

Output

5 0

3 2 4 1 5

0 1

0 2

1 3

1 4

10


Added by:Ha Minh Ngoc
Date:2020-06-15
Time limit:1s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
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