Stevie : "The more you play with Christmas Trees, the more addicted you are to them. Let's go on". Legends serve a club selflessly for ages without any noise off the pitch. Do you remember the headed goal vs the Gunners with a highly bandaged head by this guy : ?

You are given a Tree T consisting of N nodes where node i of the tree has number $A[i]$ written on it. Now, you need to process 2 kinds of queries on this tree.

$1 \space X \space Y$ : Update the number written on node with index X to Y

$2 \space U \space V \space K$ : Find if the product of number written on each nodes lying on the path from node U to V is divisible by the number K.

The answer to the second kind of query is either a YES or NO .

Can you answer all the given queries efficiently?

Input Format :

The first line contains 2 space separated integer N and Q denoting the number of nodes in tree T and the number of queries respectively.

The next line contains N space separated integers, where the $i^{th}$ integer denotes the number initially written on node i i.e. $A[i]$

Each of the next $N-1$ lines contains 2 space separated integers U and V denoting an undirected edge between nodes with index U and V in tree T.

It is guaranteed that the input edges are such that it always forms a valid tree.

Each of the next Q lines contains a query of either of the two types on a single line.

$1^{st}$ type : $1 \space X \space Y$

$2^{nd}$ type : $2 \space U \space V \space K$

Output Format:

Print the answer to each query of type 2 in the order they appear in the input on a new line. The answer to the queries shall be either a YES or a NO.

Constraints :

$1 \le N,Q \le 100,000$

$2 \le A[i],Y ,K \le 200,000$

$1 \le U,V,X \le N$