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 x1 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.