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..., 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 $\text{[math]}$ , 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 ≤ 2·10⁵, 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, ..., 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 ≤ 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:
- $\text{[math]}$ ,
- $\text{[math]}$ ,
- $\text{[math]}$ .
t = 2: Second line contains single integer a (1 ≤ a < 2³⁰) using which x can be generated using the formula given below:
- $\text{[math]}$ .

The ans_i is the answer for the i-th query, assume that ans₀ = 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 $\text{[math]}$ 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.

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

Can Bash Save the Day?

Examples