DYNALCA - Dynamic LCA

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A forest of rooted trees initially consists of N (1 ≤ N ≤ 100,000) single-vertex trees. The vertices are numbered from 1 to N.

You must process the following queries, where (1 ≤ A, B ≤ N) :

  • link A B : add an edge from vertex A to B, making A a child of B, where initially A is a root vertex, A and B are in different trees.
  • cut A : remove edge from A to its parent, where initially A is a non-root vertex.
  • lca A B : print the lowest common ancestor of A and B, where A and B are in the same tree.

Input

The first line of input contains the number of initial single-vertex trees N and the number of queries M (1 ≤ M ≤ 100,000). The following M lines contain queries.

Output

For each lca query output the lowest common ancestor (vertex number between 1 and N).

Example

Input:
5 9
lca 1 1
link 1 2
link 3 2
link 4 3
lca 1 4
lca 3 4
cut 4
link 5 3
lca 1 5

Output:
1
2
3
2



Added by:Andrey Naumenko
Date:2011-05-02
Time limit:0.367s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ASM64