You are given a tree with root node as 1. Every edge in the tree is undirected. Each node has been assigned a value. You have to handle two kinds of queries.

1 X Y : change value of node X to Y

0 X Y : Check whether the path from node X to node Y is dancing. Path is dancing if all values form alternating sequence while travelling from node X to node Y.

Eg. of alternating values sequence: 4 9 6 7 2 100 18.

Input
First line contains a number N and Q as input. Next N-1 lines contains u and v denoting there is an undirected edge between node u and v. Next line contains N integers denoting value of each node

Output
Output for only query type 0 u v whether the path from node u to v is alternating or not . Output should be YES or NO

Constraints
1≤ N ≤ 5*10^4
1≤ u ≤ v ≤ N

1≤ q ≤ 10^5
0≤ value of node ≤ 100