Problem1296--Diverging Directions

1296: Diverging Directions

Time Limit: 2 Sec  Memory Limit: 256 MB
Submit: 0  Solved: 0
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Description

time limit per test
3 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

You are given a directed weighted graph with n nodes and 2n-2 edges. The nodes are labeled from 1 to n, while the edges are labeled from 1 to 2n-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≤200000), the number of nodes, and the number of queries, respectively.

The next 2n-2 integers will contain 3 integers ai,bi,ci, denoting a directed edge from node ai to node bi with weight ci.

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 bi=1.

More specifically,

  • The edges (a1,b1),(a2,b2),... (an-1,bn-1) will describe a rooted spanning tree pointing away from node 1.
  • bj=1 for n≤j≤2n-2.
  • an,an+1,...,a2n-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 106.

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

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