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: Wrong Answer)

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

namespace A
{
    partial class Program
    {
        int n, m;
        List<int> a, b;
        Dictionary<int, HashSet<int>> es;

        public struct Edge
        {
            public int from;
            public int to;
        }

        public IEnumerable<string> Solve()
        {
            var res = Slv();
            if (res == null)
            {
                yield return "-1";
            }
            else
            {
                foreach (var e in res)
                {
                    yield return e.from.ToString() + " " + e.to.ToString();
                }
            }
        }

        public List<Edge> Slv()
        {
            n = ScanInt;
            m = ScanInt;
            if (m % 2 == 1)
            {
                return null;
            }

            es = Loop(1, n).ToDictionary(x => x, x => new HashSet<int>());
            a = new List<int>();
            b = new List<int>();
            foreach (var x in Loop(m))
            {
                var aa = ScanInt;
                var bb = ScanInt;
                a.Add(aa);
                b.Add(bb);

                es[aa].Add(bb);
                es[bb].Add(aa);
            }

            var odds = new HashSet<int>(es.Where(x => x.Value.Count % 2 == 1).Select(x => x.Key));
            var evens = new HashSet<int>(es.Where(x => x.Value.Count % 2 == 0).Select(x => x.Key));
            var res = new List<Edge>();

            var usedCount = 0;

            while (usedCount < m)
            {
                if (evens.Any() == false)
                    return null;

                var from = odds.SelectMany(x => es[x]).FirstOrDefault(x => evens.Contains(x));
                if (from == 0)
                    from = evens.First();
                var tos = es[from].OrderByDescending(x => odds.Contains(x)).Take(2).ToList();

                res.Add(new Edge() { from = from, to = tos[0] });
                res.Add(new Edge() { from = from, to = tos[1] });

                es[from].Remove(tos[0]);
                es[from].Remove(tos[1]);
                es[tos[0]].Remove(from);
                es[tos[1]].Remove(from);

                if (es[from].Any() == false)
                    evens.Remove(from);

                foreach (var to in tos)
                {
                    var toc = es[to].Count;

                    if (toc == 0)
                    {
                        odds.Remove(to);
                    }
                    else if (toc % 2 == 1)
                    {
                        odds.Add(to);
                        evens.Remove(to);
                    }
                    else
                    {
                        evens.Add(to);
                        odds.Remove(to);
                    }
                }


                usedCount += 2;
            }

            return res;
        }
    }

    class StartingPoint
    {
        static void Main(string[] args)
        {
            if (args?.Any() == true)
            {
                var assembly = Assembly.GetEntryAssembly();
                var resourceName = "AtCoderCSharp.In.txt";
                var stream = assembly.GetManifestResourceStream(resourceName);
                var streamReader = new StreamReader(stream, Encoding.UTF8);
                var str = streamReader.ReadToEnd();
                var textReader = new StringReader(str);
                Console.SetIn(textReader);
            }

            try
            {
                foreach (var s in new Program().Solve())
                {
                    Console.WriteLine(s);
                }
            }
            catch (Exception e)
            {
                Console.WriteLine(e);
                if (args?.Any() != true)
                    throw e;
            }

            if (args?.Any() == true)
                Console.ReadKey();
        }
    }

    partial class Program
    {
        public List<int> ScanInts(int count) => Enumerable.Range(0, count).Select(_ => ScanInt).ToList();
        public List<int> ScanInts(long count) => ScanInts((int)count);
        public List<long> ScanLongs(int count) => Enumerable.Range(0, count).Select(_ => Scan).ToList();
        public List<long> ScanLongs(long count) => ScanLongs((int)count);
        public int ScanInt => int.Parse(Str);
        public long Scan => long.Parse(Str);
        public double ScanDouble => (double)Scan;

        StringBuilder sb = new StringBuilder();

        public string Str => ScanStr();
        public string ScanStr()
        {
            sb.Clear();

            int r = 0;
            bool? b = null;
            do
            {
                r = Console.Read();
                b = IsBreak(r);
            } while (b == true);

            if (b == null)
                throw new Exception("input error: unexpected end of stream");

            do
            {
                sb.Append((char)r);
                r = Console.Read();
                b = IsBreak(r);
            } while (b == false);

            return sb.ToString();
        }

        bool? IsBreak(int c)
        {
            switch (c)
            {
                case -1:
                    return null;
                case (int)' ':
                case (int)'\n':
                case (int)'\r':
                    return true;
                default:
                    return false;
            }
        }

        public IEnumerable<int> Loop(int count) => Enumerable.Range(0, count);
        public IEnumerable<int> Loop(int from, int to) => Enumerable.Range(from, to - from + 1);

        public string YesNo(bool isYes) => isYes ? "Yes" : "No";

        public HashSet<T> ToHashSet<T>(IEnumerable<T> ts) => new HashSet<T>(ts);

        public int Gcm(int a, int b)
        {
            if (a < b)
                return GcmImpl(b, a);
            else
                return GcmImpl(a, b);
        }

        int GcmImpl(int a, int b)
        {
            var remainder = a % b;
            if (remainder == 0)
                return b;
            else
                return GcmImpl(b, remainder);
        }

        public int Lcm(int a, int b)
        {
            return a / Gcm(a, b) * b;
        }
    }

    class Mod
    {
        readonly int _divider = 1000000007;
        public Mod(int divider = 1000000007)
        {
            _divider = divider;
        }

        public int Add(int a, int b) => (int)Add((long)a, (long)b);
        public int Sub(int a, int b) => (int)Sub((long)a, (long)b);
        public int Mul(int a, int b) => (int)Mul((long)a, (long)b);
        public int Div(int a, int b) => (int)Div((long)a, (long)b);
        public int Pow(int a, int p) => (int)Pow((long)a, (long)p);

        public long Add(long a, long b) => (a + b) % _divider;

        public long Sub(long a, long b)
        {
            var t = (a - b) % _divider;
            if (t < 0)
                t += _divider;
            return t;
        }

        public long Mul(long a, long b) => (a * b) % _divider;

        public long Div(long a, long b) => Mul(a, Inv(b));

        public long Pow(long a, long p)
        {
            switch (p)
            {
                case 0: return 1;
                case 1: return a;
                default:
                    var halfP = p / 2;
                    var halfPowered = Pow(a, halfP);
                    var powered = Mul(halfPowered, halfPowered);
                    return p % 2 == 0 ? powered : Mul(powered, a);
            }
        }

        readonly Dictionary<long, long> invCache = new Dictionary<long, long>();
        long Inv(long a)
        {
            long cache = 0L;
            if (invCache.TryGetValue(a, out cache))
                return cache;

            var result = Pow(a, _divider - 2);
            invCache.Add(a, result);
            return result;
        }

        readonly List<int> facCache = new List<int>() { 1 };
        public int Fac(int a)
        {
            if (a < facCache.Count)
                return facCache[a];

            var val = facCache.Last();
            var start = facCache.Count;
            for (int i = start; i <= a; i++)
            {
                val = Mul(val, i);
                facCache.Add(val);
            }

            return val;
        }

        public int Perm(int n, int r)
        {
            if (n < r)
                return 0;

            if (r <= 0)
                return 1;

            int nn = Fac(n);
            int nr = Fac(n - r);
            return Div(nn, nr);
        }

        public int Comb(int n, int r)
        {
            if (n < r)
                return 0;

            if (n == r)
                return 1;

            int nn = Fac(n);
            int nr = Fac(n - r);
            int rr = Fac(r);
            return Div(Div(nn, nr), rr);
        }
    }
}