F - BOX

Score : $500$ points

Problem Statement

There are $N$ boxes numbered $1,2,\ldots,N$, and $10^{100}$ balls numbered $1,2,\dots,10^{100}$. Initially, box $i$ contains just ball $i$.

Process a total of $Q$ operations that will be performed.

There are three types of operations: $1$, $2$, and $3$.

Type $1$: Put all contents of box $Y$ into box $X$. It is guaranteed that $X \neq Y$.

1 $X$ $Y$

Type $2$: Put ball $k+1$ into box $X$, where $k$ is the current total number of balls contained in the boxes.

``` 2 $X$ ```

Type $3$: Report the number of the box that contains ball $X$.

``` 3 $X$ ```

Constraints

• All values in the input are integers.
• $2 \le N \le 3 \times 10^5$
• $1 \le Q \le 3 \times 10^5$
• For each type-$1$ operation, $1 \le X,Y \le N$ and $X \neq Y$.
• For each type-$2$ operation, $1 \le X \le N$.
• For each type-$3$ operation, ball $X$ is contained in some box at that point.
• There is at least one type-$3$ operation.

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Input

The input is given from Standard Input in the following format.
Here, $op_i$ represents the $i$-th operation.

``` $N$ $Q$ $op_1$ $op_2$ $\vdots$ $op_Q$ ```

Output

For each type-$3$ operation, print a line containing the response as an integer.

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5 10
3 5
1 1 4
2 1
2 4
3 7
1 3 1
3 4
1 1 4
3 7
3 6

5
4
3
1
3

This input contains ten operations.

• The first operation is of type $3$. Ball $5$ is in box $5$.
• The second operation is of type $1$. Put all contents of box $4$ into box $1$.
  • Box $1$ now contains balls $1$ and $4$, and box $4$ is now empty.
• The third operation is of type $2$. Put ball $6$ into box $1$.
• The fourth operation is of type $2$. Put ball $7$ into box $4$.
• The fifth operation is of type $3$. Ball $7$ is in box $4$.
• The sixth operation is of type $1$. Put all contents of box $1$ into box $3$.
  • Box $3$ now contains balls $1$, $3$, $4$, and $6$, and box $1$ is now empty.
• The seventh operation is of type $3$. Ball $4$ is in box $3$.
• The eighth operation is of type $1$. Put all contents of box $4$ into box $1$.
  • Box $1$ now contains ball $7$, and box $4$ is now empty.
• The ninth operation is of type $3$. Ball $7$ is in box $1$.
• The tenth operation is of type $3$. Ball $6$ is in box $3$.