You are given a tree with N nodes. Each node x has a value \(V_x\) associated with it.

You will also be given Q queries of two types:

• 0 a x : Set \(V_a\) to x
• 1 a b c : Find number of nodes on the unique path from a to b with value v such that \(gcd(v, c) = 1\)

Input Format:

The first line contains two integers, N and Q

The second line contains N space separated integers, where the \(i^{th}\) of them represents the value of node i.

Next \(N - 1\) lines contain two integers a and b, denoting that there is an undirected edge between nodes a and b.

Next Q lines contains a query in either of the above two formats.

Constraints:

\(1 \le N, Q \le 10^5\)

\(1 \le v \le 5000\) where v is the value of any node at any given time

For query of type 0, \(1 \le a \le N\) and \(1 \le x \le 5000\)

For query of type 1, \(1 \le a, b \le N\) and \(1 \le c \le 5000\)

Output Format:

For each query of the second type, output as answer a single integer denoting the answer to that query.

Note: It is recommended to use faster I/O methods.