Given an undirected graph, your task is to choose a direction for each edge so that in the resulting directed graph each node has an even outdegree. The outdegree of a node is the number of edges coming out of that node.
The first input line has two integers $n$ and $m$ : the number of nodes and edges. The nodes are numbered $1,2,\dots,n$ .
After this, there are $m$ lines describing the edges. Each line has two integers $a$ and $b$ : there is an edge between nodes $a$ and $b$ .
You may assume that the graph is simple, i.e., there is at most one edge between any two nodes and every edge connects two distinct nodes.
Print $m$ lines describing the directions of the edges. Each line has two integers $a$ and $b$ : there is an edge from node $a$ to node $b$ . You can print any valid solution.
If there are no solutions, only print IMPOSSIBLE .
4 4 1 2 2 3 3 4 1 4· \n · \n · \n · \n · \n
1 2 3 2 3 4 1 4· \n · \n · \n · \n