Light Heavy Edges

You are given a tree with $n$ vertices. Each edge of the tree is either a light edge or a heavy edge. You must perform $m$ operations on the tree. Initially, all edges are light edges. There are two kinds of operations.

1. You are given two vertices $a$ and $b$. For every vertex $x$ on the path between $a$ and $b$ (including $a$ and $b$ themselves), turn all edges connected to $x$ into light edges. Also turn all edges on the path between $a$ and $b$ into heavy edges.

2. You are given two vertices $a$ and $b$. Compute the number of heavy edges on the path between $a$ and $b$.

The first line contains an integer $T$, the number of test cases. Each test case starts with a line containing two integers $n$ and $m$, where $n$ is the number of vertices and $m$ is the number of operations.

The next $n-1$ lines each contain two integers $u$ and $v$, describing an edge of the tree.

The next $m$ lines each contain three integers $op_i$, $a_i$, $b_i$, describing an operation. $op_i = 1$ means an operation of the first type, and $op_i = 2$ means an operation of the second type.

It is guaranteed that $a_i \ne b_i$ in every operation.

For each operation of the second type, print the answer on its own line.

For all test sets, $T \le 3$ and $1 \le n,m \le 10^5$.