Happy Tree Party

Description:

Input:

The first line of the input contains integers, n and m (2 ≤ n ≤ 200 000, 1 ≤ m ≤ 200 000) — the number of vertecies in the tree granted to Bogdan by his mom and the number of guests that came to the party respectively.

Next n - 1 lines contain the description of the edges. The i-th of these lines contains three integers u_i, v_i and x_i (1 ≤ u_i, v_i ≤ n, u_i ≠ v_i, 1 ≤ x_i ≤ 10¹⁸), denoting an edge that connects vertecies u_i and v_i, with the number x_i initially written on it.

The following m lines describe operations, requested by Bogdan's guests. Each description contains three or four integers and has one of the two possible forms:

• 1 a_i b_i y_i corresponds to a guest, who chooses the operation of the first type.
• 2 p_i c_i corresponds to a guests, who chooses the operation of the second type.

It is guaranteed that all the queries are correct, namely 1 ≤ a_i, b_i ≤ n, 1 ≤ p_i ≤ n - 1, 1 ≤ y_i ≤ 10¹⁸ and 1 ≤ c_i < x_pi, where x_pi represents a number written on edge p_i at this particular moment of time that is not necessarily equal to the initial value x_pi, as some decreases may have already been applied to it. The edges are numbered from 1 to n - 1 in the order they appear in the input.

Output:

For each guest who chooses the operation of the first type, print the result of processing the value y_i through the path from a_i to b_i.

Sample Input:

6 6
1 2 1
1 3 7
1 4 4
2 5 5
2 6 2
1 4 6 17
2 3 2
1 4 6 17
1 5 5 20
2 4 1
1 5 1 3

Sample Output:

2
4
20
3

Sample Input:

5 4
1 2 7
1 3 3
3 4 2
3 5 5
1 4 2 100
1 5 4 1
2 2 2
1 1 3 4

Sample Output:

2
0
2

Note:

Initially the tree looks like this:

The response to the first query is: = 2

After the third edge is changed, the tree looks like this:

The response to the second query is: = 4

In the third query the initial and final vertex coincide, that is, the answer will be the initial number 20.

After the change in the fourth edge the tree looks like this:

In the last query the answer will be: = 3