CSES - Path Queries II
• Time limit: 1.00 s
• Memory limit: 512 MB
You are given a tree consisting of $n$ nodes. The nodes are numbered $1,2,\ldots,n$. Each node has a value.

1. change the value of node $s$ to $x$
2. find the maximum value on the path between nodes $a$ and $b$.
Input

The first input line contains two integers $n$ and $q$: the number of nodes and queries. The nodes are numbered $1,2,\ldots,n$.

The next line has $n$ integers $v_1,v_2,\ldots,v_n$: the value of each node.

Then there are $n-1$ lines describing the edges. Each line contains two integers $a$ and $b$: there is an edge between nodes $a$ and $b$.

Finally, there are $q$ lines describing the queries. Each query is either of the form "1 $s$ $x$" or "2 $a$ $b$".

Output

Print the answer to each query of type 2.

Constraints
• $1 \le n, q \le 2 \cdot 10^5$
• $1 \le a,b, s \le n$
• $1 \le v_i, x \le 10^9$
Example

Input:
5 3 2 4 1 3 3 1 2 1 3 2 4 2 5 2 3 5 1 2 2 2 3 5

Output:
4 3