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G. Can Bash Save the Day?
time limit per test
5 seconds
memory limit per test
768 megabytes
input
standard input
output
standard output

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 , 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

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:
    • ,
    • ,
    • .
  • t = 2: Second line contains single integer a (1 ≤ a < 230) using which x can be generated using the formula given below:
    • .

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 operation means bitwise exclusive OR.

Output

For each query of type 1, output a single integer in a separate line, denoting the answer to the query.

Example
Input
5 5
4 5 1 3 2
4 2 4
1 3 9
4 1 4
4 5 2
1
1 5 4
1
22 20 20
2
38
2
39
1
36 38 38
Output
23
37
28
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