Description:
Whoa! You did a great job helping Team Rocket who managed to capture all the Pokemons sent by Bash. Meowth, part of Team Rocket, having already mastered the human language, now wants to become a master in programming as well. He agrees to free the Pokemons if Bash can answer his questions.
Initially, Meowth gives Bash a weighted tree containing n nodes and a sequence a1, a2..., an which is a permutation of 1, 2, ..., n. Now, Mewoth makes q queries of one of the following forms:
- 1 l r v: meaning Bash should report $$\sum_{i=l}^{r} dist(a_i, v)$$, where dist(a, b) is the length of the shortest path from node a to node b in the given tree.
- 2 x: meaning Bash should swap ax and ax + 1 in the given sequence. This new sequence is used for later queries.
Help Bash to answer the questions!
Input Format:
The first line contains two integers n and q (1 ≤ n ≤ 2·105, 1 ≤ q ≤ 2·105) — the number of nodes in the tree and the number of queries, respectively.
The next line contains n space-separated integers — the sequence a1, a2, ..., an which is a permutation of 1, 2, ..., n.
Each of the next n - 1 lines contain three space-separated integers u, v, and w denoting that there exists an undirected edge between node u and node v of weight w, (1 ≤ u, v ≤ n, u ≠ v, 1 ≤ w ≤ 106). It is guaranteed that the given graph is a tree.
Each query consists of two lines. First line contains single integer t, indicating the type of the query. Next line contains the description of the query:
- t = 1: Second line contains three integers a, b and c (1 ≤ a, b, c < 230) using which l, r and v can be generated using the formula given below: $$l = (ans_{i-1} \bmod 2^{30}) \oplus a$$, $$r = ( ans_{i-1} \bmod 2^{30} ) \oplus b$$, $$v = (ans_{i-1} \bmod 2^{30}) \oplus c$$.
- t = 2: Second line contains single integer a (1 ≤ a < 230) using which x can be generated using the formula given below: $$x = (ans_{i-1} \bmod 2^{30}) \oplus a$$.
The ansi is the answer for the i-th query, assume that ans0 = 0. If the i-th query is of type 2 then ansi = ansi - 1. It is guaranteed that:
- for each query of type 1: 1 ≤ l ≤ r ≤ n, 1 ≤ v ≤ n,
- for each query of type 2: 1 ≤ x ≤ n - 1.
The $$\bigcirc$$ operation means bitwise exclusive OR.
Output Format:
For each query of type 1, output a single integer in a separate line, denoting the answer to the query.
Note:
In the sample, the actual queries are the following:
- 1 1 5 4
- 1 1 3 3
- 2 3
- 2 2
- 1 1 3 3