You are given a rooted tree \(T\) of \(n\) nodes and a graph \(G\) of \(n\) nodes. Initially, the graph \(G\) has no edges. There are two types of queries:

\(1\ x\ y\ w\): Add an edge of weight \(w\) between nodes \(x\) and \(y\) in \(G\)
\(2\ v\ p\): Consider that the edge between \(v\) and its parent in \(T\) is deleted which decomposes \(T\) into 2 connected components. You need to find the sum of weights of all edges like \(x\) in \(G\) such that:
- The weight of \(x\) is divisible by \(p\)
- If an edge is added in \(T\) between the same endpoints as \(x\) then again we will get a tree (it will connect the two components). Note that the edge is deleted only for that particular query.

Input:

First line: Two integers \(n, q (1 \le n \le 200\ 000, 1 \le q \le 300\ 000)\)
Second line: \(n-1\) integers where \((i)th\) integer is the number of the parent of \((i + 1)th\) node. \(1\) is the root of the tree.
Next \(q\) lines: Contains a description of queries. One query per line as described in the question \((1 \le w,p \le 1\ 000\ 000, 1 \le x, y \le n, 2 \le v \le n)\), \(p\) is prime
The graph \(G\) may have self-loops and multiple edges.
Queries are encrypted, hence you have to answer queries online. If \(lastAns\) is the answer of the last query of type 2 (zero if not present), then you must decrypt queries as follows:
- \(1\ x'\ y'\) must be decrypted as \(x = (x' + lastAns - 1) \mod n + 1, y = (y' + lastAns - 1) \mod n + 1\)
- \(2\ v'\) must be decrypted as \(v = (v' + lastAns - 1) \mod (n - 1) + 2\).

Output:
For each query of the second type, print the answer in a seperate line.