There’s not much time left until the “Iset” tower opens for business,
but a computer network is not yet installed in the building.
The network is expected to be very robust and should
have lots of branches. There are N nodes in the tower that should be
connected with this network. These nodes were planned to be connected
with M direct links, with no more than one direct link between
each pair of nodes.
To save some time, it was decided that only the links that are required
to make a connected network will be installed; all the remaining wires
are going to be laid after the opening ceremony.
In order to be efficient network should have satisfy one more requirement:
the maximal distance between it’s nodes must be as small as posible.
Distance between
a pair of nodes A and B is defined as the number of intermediate nodes on
the path from the node A to the node B.
Input
The first line contains two integers N (2 ≤ N ≤ 100) and
M (1 ≤ M ≤ 10000).
The following M lines describe the initial planned network layout. Each
of these lines contains a pair of integers — numbers of nodes that are
connected with a direct link. Nodes are numbered from 1 to N.
This network layout is guaranteed to be connected, and there are no links
connecting a node with itself.
Output
The new network layout (in the same format).
Sample
input  output 

4 4
1 2
2 3
2 4
3 4
 1 2
2 3
2 4

Problem Author: Sergey Pupyrev
Problem Source: The XIIth USU Programing Championship, October 6, 2007