CSES - Even Outdegree Edges
• Time limit: 1.00 s
• Memory limit: 512 MB
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.

Input

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.

Output

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".

Constraints
• $1 \le n \le 10^5$
• $1 \le m \le 2 \cdot 10^5$
• $1 \le a,b \le n$
Example

Input:
4 4 1 2 2 3 3 4 1 4

Output:
1 2 3 2 3 4 1 4