Problem C
Colorful Tree

Your task is to maintain a colorful tree and process queries.

At the beginning, there is only one vertex numbered $1$ with color $C$ on the tree. Then there are $q$ operations of two types coming in order:

• $0$ $x$ $c$ $d$: Add a new vertex indexed $(n+1)$ with color $c$ to the tree, where $n$ is the current number of existing vertices. An edge connecting vertex $x$ and $(n+1)$ with length $d$ will also be added to the tree.

• $1$ $x$ $c$: Change the color of vertex $x$ to $c$.

After each operation, you should find a pair of vertices $u$ and $v$ ($1 \le u, v \le n$) with different colors in the current tree so that the distance between $u$ and $v$ is as large as possible.

The distance between two vertices $u$ and $v$ is the length of the shortest path from $u$ to $v$ on the tree.

Input

There are multiple test cases. The first line of the input contains an integer $T$ indicating the number of test cases. For each test case:

The first line of the input contains two integers $q$ and $C$ ($1 \le q \le 5 \times 10^5$, $1 \le C \le q$) indicating the number of operations and the initial color of vertex $1$.

For the following $q$ lines, each line describes an operation taking place in order with $3$ or $4$ integers.

• If the $i$-th line contains $4$ integers $0$, $x_i$, $c_i$ and $d_i$ ($1 \le x_i \le n$, $1 \le c_i \le q$, $1 \le d \le 10^9$), the $i$-th operation will add a new vertex $(n + 1)$ with color $c_i$ to the tree and connect it to vertex $x_i$ with an edge of length $d_i$.

• If the $i$-th line contains $3$ integers $1$, $x_i$ and $c_i$ ($1 \le x_i \le n$, $1 \le c_i \le q$), the $i$-th operation will change the color of vertex $x_i$ to $c_i$.

It’s guaranteed that the sum of $q$ of all test cases will not exceed $5 \times 10^5$.

Output

For each operation output the maximum distance between two vertices with different colors. If no valid pair exists output $0$ instead.

2
1 1
0 1 1 1
5 1
0 1 1 1
0 1 2 1
0 3 3 1
1 4 1
1 3 1

0
0
2
3
2
0