Problem:
Score : 700 points

Problem Statement

You are given a simple connected undirected graph with N vertices and M edges. The vertices are numbered 1 to N, and the i-th edge connects Vertex A_i and Vertex B_i.
Takahashi will assign one of the two possible directions to each of the edges in the graph to make a directed graph.
Determine if it is possible to make a directed graph with an even number of edges going out from every vertex. If the answer is yes, construct one such graph.

Notes

An undirected graph is said to be simple when it contains no self-loops or multiple edges.

Constraints

2 \leq N \leq 10^5

N-1 \leq M \leq 10^5

1 \leq A_i,B_i \leq N (1\leq i\leq M)

The given graph is simple and connected.

Input

Input is given from Standard Input in the following format:

N M
A_1 B_1
:
A_M B_M

Output

If it is impossible to assign directions to satisfy the requirement, print -1.
Otherwise, print an assignment of directions that satisfies the requirement, in the following format:

C_1 D_1
:
C_M D_M

Here each pair (C_i, D_i) means that there is an edge directed from Vertex C_i to Vertex D_i. The edges may be printed in any order.

Sample Input 1

4 4
1 2
2 3
3 4
4 1

Sample Output 1

1 2
1 4
3 2
3 4

After this assignment of directions, Vertex 1 and 3 will each have two outgoing edges, and Vertex 2 and 4 will each have zero outgoing edges.

Sample Input 2

5 5
1 2
2 3
3 4
2 5
4 5

Sample Output 2

-1

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.*;
import java.util.*;

class Edge {
  final int id, dst;
  
  Edge(int id, int dst) {
    this.id = id;
    this.dst = dst;
  }
}

class Solver {
  final int n, m;
  final int[][] abs;
  
  List<List<Edge>> graph;
  boolean[] visitedNode;
  boolean[] visitedEdge;
  List<Integer> edgeStack;
  List<String> output;
  
  Solver(int n, int m, int[][] abs) {
    this.n = n;
    this.m = m;
    this.abs = abs;
  }
  
  private void assignDirection(int edgeId1, int edgeId2) {
    int[] indexes = new int[]{
      abs[edgeId1][0],
      abs[edgeId1][1],
      abs[edgeId2][0],
      abs[edgeId2][1]
    };
    int srcIndex = 0;
    for (int i = 0; i < 4; i++) {
      for (int j = i+1; j < 4; j++) {
        if (indexes[i] == indexes[j]) {
          srcIndex = indexes[i];
        }
      }
    }
    if (srcIndex == 0) {
      throw new RuntimeException();
    }
    for (int index : indexes) {
      if (index == srcIndex) {
        continue;
      }
      output.add(String.format("%d %d", srcIndex, index));
    }
  }
  
  private void mightAssignDirection() {
    if (edgeStack.size() < 4) {
      return;
    }
    int edgeId1 = edgeStack.get(edgeStack.size() - 1);
    int edgeId2 = edgeStack.get(edgeStack.size() - 2);
    int edgeId3 = edgeStack.get(edgeStack.size() - 3);
    int edgeId4 = edgeStack.get(edgeStack.size() - 4);
    if ((edgeId1 == edgeId2 && edgeId3 == edgeId4)
        || (edgeId1 == edgeId4 && edgeId2 == edgeId3)) {
      edgeStack.remove(edgeStack.size() - 1);
      edgeStack.remove(edgeStack.size() - 1);
      edgeStack.remove(edgeStack.size() - 1);
      edgeStack.remove(edgeStack.size() - 1);
      assignDirection(edgeId1, edgeId3);
    }
  }
  
  private void edgeDfs(int index) {
    if (visitedNode[index]) {
      return;
    }
    visitedNode[index] = true;
    for (Edge edge : graph.get(index)) {
      if (visitedEdge[edge.id]) {
        continue;
      }
      visitedEdge[edge.id] = true;
      
      edgeStack.add(edge.id);
      edgeDfs(edge.dst);
      edgeStack.add(edge.id);
      
      mightAssignDirection();
    }
  }
  
  public List<String> solve() {
    if (m % 2 == 1) {
      return Arrays.asList("-1");
    }
    
    graph = new ArrayList<>();
    visitedNode = new boolean[n + 1];
    visitedEdge = new boolean[m];
    edgeStack = new ArrayList<>();
    output = new ArrayList<>();
    for (int i = 0; i <= n; i++) {
      graph.add(new ArrayList<>());
    }
    for (int i = 0; i < m; i++) {
      int a = abs[i][0];
      int b = abs[i][1];
      graph.get(a).add(new Edge(i, b));
      graph.get(b).add(new Edge(i, a));
    }
    edgeDfs(1);
    return output;
  }
}

public class Main {
  private static void execute(ContestReader reader, PrintWriter out) {
    int n = reader.nextInt();
    int m = reader.nextInt();
    int[][] abs = reader.nextInt(m, 2);
    for (String line : new Solver(n, m, abs).solve()) {
      out.println(line);
    }
  }
  
  public static void main(String[] args) {
    ContestReader reader = new ContestReader(System.in);
    PrintWriter out = new PrintWriter(System.out);
    execute(reader, out);
    out.flush();
  }
}

class ContestReader {
  private BufferedReader reader;
  private StringTokenizer tokenizer;
  
  ContestReader(InputStream in) {
    reader = new BufferedReader(new InputStreamReader(in));
  }
  
  public String next() {
    while (tokenizer == null || !tokenizer.hasMoreTokens()) {
      try {
        tokenizer = new java.util.StringTokenizer(reader.readLine());
      } catch (Exception e) {
        throw new RuntimeException(e);
      }
    }
    return tokenizer.nextToken();
  }
  
  public int nextInt() {
    return Integer.parseInt(next());
  }
  
  public long nextLong() {
    return Long.parseLong(next());
  }
  
  public double nextDouble() {
    return Double.parseDouble(next());
  }
  
  public String[] next(int n) {
    String[] array = new String[n];
    for (int i = 0; i < n; i++) {
      array[i] = next();
    }
    return array;
  }
  
  public int[] nextInt(int n) {
    int[] array = new int[n];
    for (int i = 0; i < n; i++) {
      array[i] = nextInt();
    }
    return array;
  }
  
  public long[] nextLong(int n) {
    long[] array = new long[n];
    for (int i = 0; i < n; i++) {
      array[i] = nextLong();
    }
    return array;
  }
  
  public double[] nextDouble(int n) {
    double[] array = new double[n];
    for (int i = 0; i < n; i++) {
      array[i] = nextDouble();
    }
    return array;
  }
  
  public char[] nextCharArray() {
    return next().toCharArray();
  }
  
  public int[][] nextInt(int n, int m) {
    int[][] matrix = new int[n][m];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        matrix[i][j] = nextInt();
      }
    }
    return matrix;
  }
  
  public long[][] nextLong(int n, int m) {
    long[][] matrix = new long[n][m];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        matrix[i][j] = nextLong();
      }
    }
    return matrix;
  }
  
  public double[][] nextDouble(int n, int m) {
    double[][] matrix = new double[n][m];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        matrix[i][j] = nextDouble();
      }
    }
    return matrix;
  }
  
  public char[][] nextCharArray(int n) {
    char[][] matrix = new char[n][];
    for (int i = 0; i < n; i++) {
      matrix[i] = next().toCharArray();
    }
    return matrix;
  }
}