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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 :

\( 1 \le N,Q \le 100,000 \)

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

\( 1 \le U,V,X \le N \)