A14860. Permutation and Queries

You are given a permutation $p$ of $n$ elements. A permutation of $n$ elements is an array of length $n$ containing each integer from $1$ to $n$ exactly once. For example, $[1, 2, 3]$ and $[4, 3, 5, 1, 2]$ are permutations, but $[1, 2, 4]$ and $[4, 3, 2, 1, 2]$ are not permutations. You should perform $q$ queries.

There are two types of queries:

- $1$ $x$ $y$ — swap $p_x$ and $p_y$ .
- $2$ $i$ $k$ — print the number that $i$ will become if we assign $i = p_i$ $k$ times.

The first line contains two integers $n$ and $q$ ( $1 \le n, q \le 10^5$ ).

The second line contains $n$ integers $p_1, p_2, \dots, p_n$ .

Each of the next $q$ lines contains three integers. The first integer is $t$ ( $1 \le t \le 2$ ) — type of query. If $t = 1$ , then the next two integers are $x$ and $y$ ( $1 \le x, y \le n$ ; $x \ne y$ ) — first-type query. If $t = 2$ , then the next two integers are $i$ and $k$ ( $1 \le i, k \le n$ ) — second-type query.

It is guaranteed that there is at least one second-type query.

For every second-type query, print one integer in a new line — answer to this query.

In the first example $p = \{5, 3, 4, 2, 1\}$ .

The first query is to print $p_3$ . The answer is $4$ .

The second query is to print $p_{p_1}$ . The answer is $1$ .

The third query is to swap $p_1$ and $p_3$ . Now $p = \{4, 3, 5, 2, 1\}$ .

The fourth query is to print $p_{p_1}$ . The answer is $2$ .