You are given a tree consisting of $n$ nodes. The nodes are numbered $1,2,\ldots,n$ . Each node has a value.

Your task is to process following types of queries:

change the value of nodestoxfind the maximum value on the path between nodesaandb.

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 $a$ $b$ ".

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

Print the answer to each query of type 2.