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 C# (Mono 4.6.2.0) (judge verdict: Time Limit Exceeded)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Diagnostics;
using System.IO;
using System.Linq;
using System.Text;

namespace AGC035B
{
    class Program
    {
        public static void Solve(Input input)
        {
            var n = input.NextInt();
            var m = input.NextInt();

            // V2が辺の状態を表すことにする
            // 0: 未定、1: 吸い込み、2: 吐き出し
            var connection = Enumerable.Range(0, n)
                .Select(_ => new Dictionary<int, int>())
                .ToArray();

            if (m % 2 != 0)
            {
                Console.WriteLine(-1);
                return;
            }

            for (int i = 0; i < m; i++)
            {
                var a = input.NextInt() - 1;
                var b = input.NextInt() - 1;

                connection[a].Add(b, 0);
                connection[b].Add(a, 0);
            }

            dfs(connection, new bool[n], -1, 0);

            for (int i = 0; i < n; i++)
            {
                var node = connection[i];
                foreach (var e in node.Where(x => x.Value == 2))
                {
                    Console.WriteLine($"{i + 1} {e.Key + 1}");

                }
            }
        }

        static void dfs(Dictionary<int, int>[] connection, bool[] visited, int from, int s)
        {
            if (visited[s])
            {
                return;
            }

            visited[s] = true;

            var keys1 = connection[s].Keys.ToArray();
            foreach (var e in keys1)
            {
                dfs(connection, visited, s, e);
            }

            // 出次数
            var c = connection[s].Count(x => x.Value == 2) % 2;
            var keys = connection[s].Where(x => x.Value == 0).Select(x => x.Key).ToArray();
            for (int i = 0; i < keys.Length; i++)
            {
                var e = keys[i];
                if (c > 0)
                {
                    // 吐き出しとする
                    connection[s][e] = 2;
                    connection[e][s] = 1;
                    c--;
                }
                else
                {
                    // 吸い出しとする
                    connection[s][e] = 1;
                    connection[e][s] = 2;
                }

            }
        }

        /// <summary>
        /// 値を書き換え可能なTuple（ぐらいのイメージ）
        /// </summary>
        /// <typeparam name="T"></typeparam>
        /// <typeparam name="U"></typeparam>
        public class Pair<T, U> : IComparable<Pair<T, U>>, IEquatable<Pair<T, U>>
            where T : IComparable<T>
            where U : IComparable<U>
        {
            public T V1 { get; set; }
            public U V2 { get; set; }

            public Pair(T v1, U v2)
            {
                this.V1 = v1;
                this.V2 = v2;
            }

            public Pair(Pair<T, U> src)
            {
                this.V1 = src.V1;
                this.V2 = src.V2;
            }

            public int CompareTo(Pair<T, U> other)
            {
                var r = this.V1.CompareTo(other.V1);
                if (r == 0) r = this.V2.CompareTo(other.V2);

                return r;
            }

            public bool Equals(Pair<T, U> other)
            {
                return other != null && this.CompareTo(other) == 0;
            }

            public override string ToString()
            {
                return $"{V1} {V2}";
            }

            public override bool Equals(object obj)
            {
                return Equals(obj as Pair<T, U>);
            }

            public override int GetHashCode()
            {
                var hashCode = 1989511945;
                hashCode = hashCode * -1521134295 + V1.GetHashCode();
                hashCode = hashCode * -1521134295 + V2.GetHashCode();
                return hashCode;
            }

            public static bool operator ==(Pair<T, U> a, Pair<T, U> b)
            {
                if (object.ReferenceEquals(a, null))
                {
                    return object.ReferenceEquals(b, null);
                }

                return a.Equals(b);
            }

            public static bool operator !=(Pair<T, U> a, Pair<T, U> b)
                => !(a == b);
            public static bool operator <(Pair<T, U> a, Pair<T, U> b)
                => a.CompareTo(b) < 0;
            public static bool operator <=(Pair<T, U> a, Pair<T, U> b)
                => a.CompareTo(b) <= 0;
            public static bool operator >(Pair<T, U> a, Pair<T, U> b)
                => a.CompareTo(b) > 0;
            public static bool operator >=(Pair<T, U> a, Pair<T, U> b)
                => a.CompareTo(b) >= 0;
        }

        #region Main
        public static void Main(string[] args)
        {
            // 出力が少ないときはこれをセットする方が時間かかるけれど
            // その場合は出力がボトルネックになっていないので、まあ良しとする
            var needsFlushOutput = true;
            if (needsFlushOutput)
            {
                // 細かく出力しないようにする
                var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
                Console.SetOut(sw);
            }

            // 通常は引数無しで、ファイルから読み出したい場合はpath指定する
            var input = new Input();
            // 仮想的に標準入力をセットする
            //input.SetText("");

            Solve(input);

            Console.Out.Flush();
        }
        #endregion

        #region Competitive Template
#pragma warning disable CS0414
        static readonly int MOD = (int)1e9 + 7;
#pragma warning restore CS0414

        public class Input
        {
            // 変な改行コードがたまに混じっているので、一応セパレート指定する
            // スペース単独指定の方がもちろん早い
            static readonly char[] separator = { ' ', '\r', '\n' };
            Queue<string> q { get; set; }
            StreamReader sr;

            /// <summary>
            /// 特定のファイルから読み出したい場合はpath指定する
            /// </summary>
            /// <param name="path"></param>
            public Input(string path = "")
            {
                q = new Queue<string>();

                if (string.IsNullOrEmpty(path))
                {
                    sr = new StreamReader(Console.OpenStandardInput());
                }
                else
                {
                    sr = new StreamReader(path);
                }
            }

            /// <summary>
            /// 入力予約
            /// </summary>
            /// <param name="items"></param>
            public void SetText(IEnumerable<string> items)
            {
                foreach (var item in items)
                {
                    SetText(item);
                }
            }

            /// <summary>
            /// 入力予約
            /// </summary>
            /// <param name="s"></param>
            /// <returns></returns>
            public bool SetText(string s)
            {
                if (s == null) return false;

                foreach (var elem in s.Trim().Split(separator, StringSplitOptions.RemoveEmptyEntries))
                {
                    q.Enqueue(elem);
                }

                return true;
            }

            /// <summary>
            /// 要素が存在するか
            /// </summary>
            /// <returns></returns>
            public bool Any()
                => q.Any() || read();


            /// <summary>
            /// 内部queueに入力からの値をsplitして格納する
            /// </summary>
            /// <returns></returns>
            bool read()
            {
                var s = sr.ReadLine();
                if (s == null) return false;

                foreach (var elem in s.Trim().Split(separator, StringSplitOptions.RemoveEmptyEntries))
                {
                    q.Enqueue(elem);
                }

                if (!q.Any()) return read();

                return true;
            }

            /// <summary>
            /// 次のstringを一つ読み込む
            /// </summary>
            /// <returns></returns>
            public string Next()
            {
                if (!q.Any())
                {
                    if (!read())
                    {
                        return "";
                    }
                }

                return q.Dequeue();
            }

            /// <summary>
            /// 指定個数queueにたまるまでenqueueし続ける
            /// </summary>
            /// <param name="n"></param>
            /// <returns></returns>
            bool accumulate(int n)
            {
                while (q.Count() < n)
                {
                    if (!read()) return false;
                }

                return true;
            }

            public int NextInt() => int.Parse(Next());
            public long NextLong() => long.Parse(Next());
            public double NextDouble() => double.Parse(Next());

            /// <summary>
            /// n個の要素をparseして、それぞれにoffsetをaddした配列を返す
            /// </summary>
            /// <typeparam name="T"></typeparam>
            /// <param name="n"></param>
            /// <param name="offset"></param>
            /// <param name="parse"></param>
            /// <param name="add"></param>
            /// <returns></returns>
            T[] NextT<T>(int n, T offset, Func<string, T> parse, Func<T, T, T> add)
            {
                if (!accumulate(n)) return null;

                var a = new T[n];

                for (int i = 0; i < n; i++)
                    a[i] = add(parse(q.Dequeue()), offset);

                return a;
            }

            public string[] Next(int n) => NextT(n, "", x => x, (x, y) => x);
            public int[] NextInt(int n, int offset = 0) => NextT(n, offset, int.Parse, (x, y) => x + y);
            public long[] NextLong(int n, long offset = 0) => NextT(n, offset, long.Parse, (x, y) => x + y);
            public double[] NextDouble(int n, double offset = 0.0) => NextT(n, offset, double.Parse, (x, y) => x + y);
        }

        static class Utils
        {
            public static void Print<T>(IEnumerable<T> ie, string sep = " ") => Console.WriteLine(string.Join(sep, ie));
            public static void Print<T>(params T[] objs) => Print(objs);
            public static T Max<T>(params T[] objs) => objs.Max();
            public static T Min<T>(params T[] objs) => objs.Min();

            public static void Swap<T>(ref T x, ref T y) where T : struct { var t = x; x = y; y = t; }
            public static void Swap<T>(IList<T> list, int i, int j) where T : struct { var t = list[i]; list[i] = list[j]; list[j] = t; }

            /// <summary>
            /// vでfillされたT[d1][d2]配列を作成する
            /// </summary>
            /// <typeparam name="T"></typeparam>
            /// <param name="d1"></param>
            /// <param name="d2"></param>
            /// <param name="v"></param>
            /// <returns></returns>
            public static T[][] Create2DArray<T>(int d1, int d2, T v = default(T))
            {
                return
                    Enumerable.Repeat(0, d1).Select(_ =>
                    Enumerable.Repeat(v, d2).ToArray()).ToArray();
            }

            /// <summary>
            /// vでfillされたT[d1][d2][d3]配列を作成する
            /// </summary>
            /// <typeparam name="T"></typeparam>
            /// <param name="d1"></param>
            /// <param name="d2"></param>
            /// <param name="d3"></param>
            /// <param name="v"></param>
            /// <returns></returns>
            public static T[][][] Create3DArray<T>(int d1, int d2, int d3, T v = default(T))
            {
                return
                    Enumerable.Repeat(0, d1).Select(_ =>
                    Enumerable.Repeat(0, d2).Select(__ =>
                     Enumerable.Repeat(v, d3).ToArray()).ToArray()).ToArray();
            }
        }
        #endregion
    }
}