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data structures

divide and conquer

graphs

trees

*3400

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G. Can Bash Save the Day?

time limit per test

5 secondsmemory limit per test

768 megabytesinput

standard inputoutput

standard outputWhoa! 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 *a*_{1}, *a*_{2}..., *a*_{n} 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
*a*_{x}and*a*_{x + 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* ≤ 2·10^{5}, 1 ≤ *q* ≤ 2·10^{5}) — the number of nodes in the tree and the number of queries, respectively.

The next line contains *n* space-separated integers — the sequence *a*_{1}, *a*_{2}, ..., *a*_{n} 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* ≤ 10^{6}). 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*< 2^{30}) using which*l*,*r*and*v*can be generated using the formula given below:- ,
- ,
- .

- t = 2: Second line contains single integer
*a*(1 ≤*a*< 2^{30}) using which*x*can be generated using the formula given below:- .

The *ans*_{i} is the answer for the *i*-th query, assume that *ans*_{0} = 0. If the *i*-th query is of type 2 then *ans*_{i} = *ans*_{i - 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

Codeforces (c) Copyright 2010-2023 Mike Mirzayanov

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