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B. Diverging Directions

time limit per test

3 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou are given a directed weighted graph with *n* nodes and 2*n* - 2 edges. The nodes are labeled from 1 to *n*, while the edges are labeled from 1 to 2*n* - 2. The graph's edges can be split into two parts.

- The first
*n*- 1 edges will form a rooted spanning tree, with node 1 as the root. All these edges will point away from the root. - The last
*n*- 1 edges will be from node*i*to node 1, for all 2 ≤*i*≤*n*.

You are given *q* queries. There are two types of queries

- 1
*i**w*: Change the weight of the*i*-th edge to*w* - 2
*u**v*: Print the length of the shortest path between nodes*u*to*v*

Given these queries, print the shortest path lengths.

Input

The first line of input will contain two integers *n*, *q* (2 ≤ *n*, *q* ≤ 200 000), the number of nodes, and the number of queries, respectively.

The next 2*n* - 2 integers will contain 3 integers *a*_{i}, *b*_{i}, *c*_{i}, denoting a directed edge from node *a*_{i} to node *b*_{i} with weight *c*_{i}.

The first *n* - 1 of these lines will describe a rooted spanning tree pointing away from node 1, while the last *n* - 1 of these lines will have *b*_{i} = 1.

More specifically,

- The edges (
*a*_{1},*b*_{1}), (*a*_{2},*b*_{2}), ... (*a*_{n - 1},*b*_{n - 1}) will describe a rooted spanning tree pointing away from node 1. -
*b*_{j}= 1 for*n*≤*j*≤ 2*n*- 2. -
*a*_{n},*a*_{n + 1}, ...,*a*_{2n - 2}will be distinct and between 2 and*n*.

The next *q* lines will contain 3 integers, describing a query in the format described in the statement.

All edge weights will be between 1 and 10^{6}.

Output

For each type 2 query, print the length of the shortest path in its own line.

Example

Input

5 9

1 3 1

3 2 2

1 4 3

3 5 4

5 1 5

3 1 6

2 1 7

4 1 8

2 1 1

2 1 3

2 3 5

2 5 2

1 1 100

2 1 3

1 8 30

2 4 2

2 2 4

Output

0

1

4

8

100

132

10

Codeforces (c) Copyright 2010-2023 Mike Mirzayanov

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