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F. Forced Online Queries Problem
time limit per test
5 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

You are given an undirected graph with $$$n$$$ vertices numbered from $$$1$$$ to $$$n$$$. Initially there are no edges.

You are asked to perform some queries on the graph. Let $$$last$$$ be the answer to the latest query of the second type, it is set to $$$0$$$ before the first such query. Then the queries are the following:

  • $$$1~x~y$$$ ($$$1 \le x, y \le n$$$, $$$x \ne y$$$) — add an undirected edge between the vertices $$$(x + last - 1)~mod~n + 1$$$ and $$$(y + last - 1)~mod~n + 1$$$ if it doesn't exist yet, otherwise remove it;
  • $$$2~x~y$$$ ($$$1 \le x, y \le n$$$, $$$x \ne y$$$) — check if there exists a path between the vertices $$$(x + last - 1)~mod~n + 1$$$ and $$$(y + last - 1)~mod~n + 1$$$, which goes only through currently existing edges, and set $$$last$$$ to $$$1$$$ if so and $$$0$$$ otherwise.

Good luck!

Input

The first line contains two integer numbers $$$n$$$ and $$$m$$$ ($$$2 \le n, m \le 2 \cdot 10^5$$$) — the number of vertices and the number of queries, respectively.

Each of the following $$$m$$$ lines contains a query of one of two aforementioned types. It is guaranteed that there is at least one query of the second type.

Output

Print a string, consisting of characters '0' and '1'. The $$$i$$$-th character should be the answer to the $$$i$$$-th query of the second type. Therefore the length of the string should be equal to the number of queries of the second type.

Examples
Input
5 9
1 1 2
1 1 3
2 3 2
1 2 4
2 3 4
1 2 4
2 3 4
1 1 3
2 4 3
Output
1010
Input
3 9
1 1 2
1 2 3
1 3 1
2 1 3
1 3 2
2 2 3
1 1 2
2 1 2
2 1 2
Output
1101
Note

The converted queries in the first example are:

  • 1 1 2
  • 1 1 3
  • 2 3 2
  • 1 3 5
  • 2 4 5
  • 1 2 4
  • 2 3 4
  • 1 2 4
  • 2 5 4

The converted queries in the second example are:

  • 1 1 2
  • 1 2 3
  • 1 3 1
  • 2 1 3
  • 1 1 3
  • 2 3 1
  • 1 2 3
  • 2 2 3
  • 2 1 2