Caisa and Tree

10000ms

262144K

Description:

Caisa is now at home and his son has a simple task for him.

Given a rooted tree with n vertices, numbered from 1 to n (vertex 1 is the root). Each vertex of the tree has a value. You should answer q queries. Each query is one of the following:

Format of the query is "1 v". Let's write out the sequence of vertices along the path from the root to vertex v: u₁, u₂, ..., u_k (u₁ = 1; u_k = v). You need to output such a vertex u_i that gcd(value of u_i, value of v) > 1 and i < k. If there are several possible vertices u_i pick the one with maximum value of i. If there is no such vertex output -1.
Format of the query is "2 v w". You must change the value of vertex v to w.

You are given all the queries, help Caisa to solve the problem.

Input:

The first line contains two space-separated integers n, q (1 ≤ n, q ≤ 10⁵).

The second line contains n integers a₁, a₂, ..., a_n (1 ≤ a_i ≤ 2·10⁶), where a_i represent the value of node i.

Each of the next n - 1 lines contains two integers x_i and y_i (1 ≤ x_i, y_i ≤ n; x_i ≠ y_i), denoting the edge of the tree between vertices x_i and y_i.

Each of the next q lines contains a query in the format that is given above. For each query the following inequalities hold: 1 ≤ v ≤ n and 1 ≤ w ≤ 2·10⁶. Note that: there are no more than 50 queries that changes the value of a vertex.

Output:

For each query of the first type output the result of the query.

Sample Input:

Sample Output:

Note:

gcd(x, y) is greatest common divisor of two integers x and y.

Informação

Provedor Codeforces

Código CF463E