There is an undirected graph with $N$ vertices and $0$ edges. The vertices are numbered $1$ to $N$.

You are given $Q$ queries to process in order. Each query is of one of the following two types:

• Type $1$: Given in the format 1 u v. Add an edge between vertices $u$ and $v$.
• Type $2$: Given in the format 2 v k. Print the $k$-th largest vertex number among the vertices connected to vertex $v$. If there are fewer than $k$ vertices connected to $v$, print -1.

The input is given from Standard Input in the following format:

$N$ $Q$

$\mathrm{query}_1$

$\mathrm{query}_2$

$\vdots$

$\mathrm{query}_Q$

Here, $\mathrm{query}_i$ is the $i$-th query and is given in one of the following formats:

$1$ $u$ $v$

$2$ $v$ $k$

Let $q$ be the number of Type $2$ queries. Print $q$ lines.

The $i$-th line should contain the answer to the $i$-th Type $2$ query.

• $1 \leq N, Q \leq 2 \times 10^5$
• In a Type $1$ query, $1 \leq u < v \leq N$.
• In a Type $2$ query, $1 \leq v \leq N$, $1 \leq k \leq 10$.
• All input values are integers.

• In the first query, an edge is added between vertices $1$ and $2$.
• In the second query, two vertices are connected to vertex $1$: $1$ and $2$. Among them, the $1$-st largest vertex number is $2$, which should be printed.
• In the third query, two vertices are connected to vertex $1$: $1$ and $2$. Among them, the $2$-nd largest vertex number is $1$, which should be printed.
• In the fourth query, two vertices are connected to vertex $1$: $1$ and $2$, which is fewer than $3$, so print -1.
• In the fifth query, an edge is added between vertices $1$ and $3$.
• In the sixth query, an edge is added between vertices $2$ and $3$.
• In the seventh query, an edge is added between vertices $3$ and $4$.
• In the eighth query, four vertices are connected to vertex $1$: $1,2,3,4$. Among them, the $1$-st largest vertex number is $4$, which should be printed.
• In the ninth query, four vertices are connected to vertex $1$: $1,2,3,4$. Among them, the $3$-rd largest vertex number is $2$, which should be printed.
• In the tenth query, four vertices are connected to vertex $1$: $1,2,3,4$, which is fewer than $5$, so print -1.