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

Input:

4 4
1 2
2 3
3 4
1 4

Output:

1 2
3 2
3 4
1 4