A rookie is curious about what the FME graph is. After some days, he learns that it is an undirected graph where the vertices are the FME students, and there is an edge between x and y if they had an affair at some moment. There is no more than one edge between each pair x and y, nor edges of the kind x x.

Suppose that someone gives you the number of vertices n and the number of edges m. With this information, can you tell if the graph is connected, if it is not, or that you are being fooled?

Input

Input consists of several cases.
Every case has the supposed numbers of vertices and edges
of an undirected graph.
You can assume 2 ≤ n ≤ 10^{9} and 0 ≤ m ≤ 10^{9}.

Output

For every case, tell if you can assure that the graph is connected, if you can assure that the graph is not connected, if it is impossible that such a graph exists, or if we are in none of those situations.

Public test cases

**Input**

4 4 142857 42 2 2 1000000000 1000000000

**Output**

connected disconnected you've been trolled impossible to know

Information

- Author
- Ferran Alet
- Language
- English
- Translator
- Original language
- Catalan
- Other languages
- Catalan
- Official solutions
- C++
- User solutions
- C++