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 ≤ 10^5)~
• 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

5 0
3 2 4 1 5
0 1
0 2
1 3
1 4

Sample Output

10