问题 A: Magma Cave

Little Q is researching an active volcano. There are $n$ caves inside the volcano, labeled by $1,2,\dots ,n$. At the very beginning, before the first volcanic activity event, there is no magma path between these caves. You will be given $q$ operations, each operation is one of the following:

• ''$\text{1 u v w}$'' ($1\le u,v\le n$, u$v$, $1\le w\le q$): A volcanic activity event comes such that a new magma path between the $u$-th cave and the $v$-th cave occurs, whose length is $w$. Here $w$ is used for identifying the magma path, so $w$ will always be pairwise different.
• ''$\text{2 k w}$'' ($1\le k<n$, $1\le w\le q$): Assume it is a undirected graph with $n$ vertices, each magma path denoting an edge, Little Q is wondering whether there exists a spanning tree whose $k$-th shortest edge is of length $w$. You are the partner of Little Q, please write a program to answer his question.

The first line contains a single integer $T$ ($1\le T\le 100$), the number of test cases. For each test case:

The first line contains two integers $n$ and $q$ ($2\le n\le 50,000$, $1\le q\le 200,000$), denoting the number of caves and the number of operations.

Each of the next $q$ lines describes an operation in formats described in the statement above.

It is guaranteed that the sum of all $n$ is at most $300,000$, and the sum of all $q$ is at most $1,000,000$.

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

NO
YES
YES
NO
YES
YES