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.ComponentModel.Design;
using System.IO;
using System.Linq;
using System.Net.NetworkInformation;
using System.Security.Cryptography;
using System.Text;
using System.Threading;
using Extensions;
using static System.Math;
using static Extensions.MathExtension;
using static Extensions.ConsoleInputExtension;
using static Extensions.ConsoleOutputExtension;

class Solver
{
    public void Solve()
    {
        //Solve Code Here
        int N = Cin, M = Cin;
        var tree = new Node[N];
        for (var i = 0; i < tree.Length; i++)
        {
            tree[i] = new Node {Id = i + 1};
        }

        for (int i = 0; i < M; i++)
        {
            int a = Cin, b = Cin;
            tree[a - 1].AddConnection(tree[b - 1]);
        }

        tree = tree.OrderBy(val => val.Connections.Count).ToArray();

        foreach (var node in tree)
        {
            Transform(node);
        }

        var fromCount = new int[N];
        foreach (var connection in Connection.AllConnections)
        {
            fromCount[connection.From.Id - 1]++;
        }

        int f = 0;
        for (var i = 0; i < N; i++)
        {
            f |= fromCount[i];
        }

        if ((f & 1) != 0)
        {
            Coutln(-1);
            return;
        }

        foreach (var connection in Connection.AllConnections)
        {
            Coutln(connection.From.Id + " " + connection.To.Id);
        }
    }

    //Other Functions Here

    private void Transform(Node node)
    {
        node.Flg = true;
        int thisFromCount = 0;
        foreach (var connection in node.Connections)
        {
            if (connection.From == node)
            {
                thisFromCount++;
            }
        }

        thisFromCount &= 1;
        foreach (var connection in node.Connections)
        {
            var other = connection.Other(node);
            if (other.Flg) continue;
            if (thisFromCount > 0)
            {
                thisFromCount--;
                connection.Swap();
            }
        }
    }
}

//Other Classes Here
class Node
{
    public bool Flg { get; set; } = false;
    public int Id { get; set; }
    public List<Connection> Connections { get; } = new List<Connection>();

    public void AddConnection(Node n)
    {
        var connection = new Connection {From = this, To = n};
        this.Connections.Add(connection);
        n.Connections.Add(connection);
    }

    public static bool operator ==(Node n1, Node n2)
    {
        return n1.Id == n2.Id;
    }

    public static bool operator !=(Node n1, Node n2)
    {
        return !(n1 == n2);
    }
}

class Connection
{
    public static List<Connection> AllConnections { get; } = new List<Connection>();
    public Node From { get; set; }
    public Node To { get; set; }

    public Connection()
    {
        AllConnections.Add(this);
    }

    public void Swap()
    {
        var tmp = From;
        From = To;
        To = tmp;
    }

    public Node Other(Node n)
    {
        return From == n ? To : From;
    }
}

#if !DEBUG
class EntryPoint
{
    static void Main(string[] args)
    {
        new Solver().Solve();
        Flush();
    }
}
#endif

class PriorityQueue<T>
{
    private readonly List<Tuple<int, T>> _list = new List<Tuple<int, T>>();
    public int Count { get; private set; } = 0;

    public PriorityQueue()
    {
        _list.Add(null);
        _list.Add(null);
        _list.Add(null);
    }

    public void Push(T item, int priority)
    {
        var itemIndex = Count++;
        _list[itemIndex] = Tuple.Create(priority, item);
        while (_list.Count < Count + 2) _list.Add(null);

        int parentIndex;
        while ((parentIndex = GetParentIndex(itemIndex)) != -1 && priority > _list[parentIndex].Item1)
        {
            Swap(itemIndex, parentIndex);
            itemIndex = parentIndex;
        }
    }

    private int GetParentIndex(int index)
    {
        if (index == 0) return -1;
        return ((index + 1) >> 1) - 1;
    }

    private Tuple<int, int> GetChildrenIndex(int index)
    {
        var item2 = (index + 1) << 1;
        var item1 = item2 - 1;
        return item2 >= _list.Count ? null : Tuple.Create(item1, item2);
    }

    public T Pop()
    {
        if (_list.Count <= 0 || _list[0] == null) throw new IndexOutOfRangeException();
        var item = _list[0].Item2;
        _list[0] = null;
        Tuple<int, int> childrenIndex;
        int index = 0;
        while ((childrenIndex = GetChildrenIndex(index)) != null &&
               (_list[childrenIndex.Item1] != null || _list[childrenIndex.Item2] != null))
        {
            if ((_list[childrenIndex.Item1]       != null && _list[childrenIndex.Item2] != null &&
                 _list[childrenIndex.Item1].Item1 > _list[childrenIndex.Item2].Item1) ||
                _list[childrenIndex.Item2] == null)
            {
                _list[index] = _list[childrenIndex.Item1];
                _list[childrenIndex.Item1] = null;
                index = childrenIndex.Item1;
            }
            else
            {
                two:
                _list[index] = _list[childrenIndex.Item2];
                _list[childrenIndex.Item2] = null;
                index = childrenIndex.Item2;
            }
        }

        Count--;
        return item;
    }

    public T Peek()
    {
        return _list[0].Item2;
    }

    private void Swap(int index1, int index2)
    {
        var tmp = _list[index1];
        _list[index1] = _list[index2];
        _list[index2] = tmp;
    }
}

struct Rational
{
    private long _numerator;
    private long _denominator;
    public long Numerator => _numerator;
    public long Denominator => _denominator;

    public Rational(long numerator, long denominator)
    {
        var gcd = GCD(numerator, denominator);
        _numerator = numerator     / gcd;
        _denominator = denominator / gcd;
    }

    public static Rational operator +(Rational a, Rational b)
    {
        return new Rational(a._numerator * b._denominator + b._numerator * a._denominator,
                            a._denominator * b._denominator);
    }

    public static Rational operator -(Rational a, Rational b)
    {
        return new Rational(a._numerator * b._denominator - b._numerator * a._denominator,
                            a._denominator * b._denominator);
    }

    public static Rational operator *(Rational a, Rational b)
    {
        return new Rational(a._numerator * b._numerator, a._denominator * b._denominator);
    }

    public static Rational operator /(Rational a, Rational b)
    {
        return new Rational(a._numerator * b._denominator, a._denominator * b._numerator);
    }

    public static explicit operator Rational(int i)
    {
        return new Rational(i, 1);
    }

    public static explicit operator Rational(long l)
    {
        return new Rational(l, 1);
    }

    public static explicit operator Rational(double d)
    {
        long denominator = 1;
        while (d % 1 != 0)
        {
            denominator *= 2;
            d *= 2;
        }

        return new Rational((long) d, denominator);
    }

    public static explicit operator Rational(float f)
    {
        long denominator = 1;
        while (f % 1 != 0)
        {
            denominator *= 2;
            f *= 2;
        }

        return new Rational((long) f, denominator);
    }
}

struct ModInt
{
    public long Value { get; }
    public static long Mod { get; set; } = 1000000000L + 7;

    public ModInt(long l)
    {
        long value = l % Mod;
        while (value < 0) value += Mod;
        Value = value % Mod;
    }

    public static implicit operator long(ModInt m)
    {
        return m.Value;
    }

    public static explicit operator ModInt(long l)
    {
        return new ModInt(l);
    }

    public static ModInt operator +(ModInt a, ModInt b)
    {
        return new ModInt(a.Value + b.Value);
    }

    public static ModInt operator -(ModInt a, ModInt b)
    {
        return new ModInt(a.Value - b.Value);
    }

    public static ModInt operator *(ModInt a, ModInt b)
    {
        return new ModInt(a.Value * b.Value);
    }

    public static ModInt operator /(ModInt a, ModInt b)
    {
        return new ModInt(a * b.Inverse());
    }

    public override string ToString()
    {
        return Value.ToString();
    }
}

static class ModIntMath
{
    public static ModInt Pow(this ModInt a, ModInt b)
    {
        var pow = b.Value;
        var m = a;
        ModInt ans = new ModInt(1);
        while (pow != 0)
        {
            if ((pow & 1) == 1)
            {
                ans *= m;
            }

            pow >>= 1;
            m *= m;
        }

        return ans;
    }

    public static ModInt Inverse(this ModInt m)
    {
        return m.Pow((ModInt) (ModInt.Mod - 2));
    }
}

class UnionFind
{
    private readonly int[] _array;

    public UnionFind(int N)
    {
        _array = new int[N];
        for (int i = 0; i < N; i++)
        {
            _array[i] = i;
        }
    }

    public int GetRootNode(int n)
    {
        if (_array[n] == n) return n;
        return _array[n] = GetRootNode(_array[n]);
    }

    public void UnionGroup(int a, int b)
    {
        var rootA = GetRootNode(a);
        var rootB = GetRootNode(b);
        if (rootA == rootB) return;
        _array[rootA] = rootB;
    }

    public bool IsSameGroup(int a, int b) => GetRootNode(a) == GetRootNode(b);

    public bool IsRoot(int n) => _array[n] == n;
}


namespace Extensions
{
    public class ConsoleInputExtension
    {
        private static readonly ConsoleInputExtension _cin = new ConsoleInputExtension();

        public static ConsoleInputExtension Cin => _cin;

        private static readonly Queue<string> _inputQueue = new Queue<string>();

        private ConsoleInputExtension()
        {
        }

        public static implicit operator string(ConsoleInputExtension _)
        {
            if (_inputQueue.Count == 0) Console.ReadLine().Split(' ').ForEach(val => _inputQueue.Enqueue(val));
            return _inputQueue.Dequeue();
        }

        public static implicit operator int(ConsoleInputExtension _)
        {
            if (_inputQueue.Count == 0) Console.ReadLine().Split(' ').ForEach(val => _inputQueue.Enqueue(val));
            return int.Parse(_inputQueue.Dequeue());
        }

        public static implicit operator long(ConsoleInputExtension _)
        {
            if (_inputQueue.Count == 0) Console.ReadLine().Split(' ').ForEach(val => _inputQueue.Enqueue(val));
            return long.Parse(_inputQueue.Dequeue());
        }

        public static implicit operator float(ConsoleInputExtension _)
        {
            if (_inputQueue.Count == 0) Console.ReadLine().Split(' ').ForEach(val => _inputQueue.Enqueue(val));
            return float.Parse(_inputQueue.Dequeue());
        }

        public static implicit operator double(ConsoleInputExtension _)
        {
            if (_inputQueue.Count == 0) Console.ReadLine().Split(' ').ForEach(val => _inputQueue.Enqueue(val));
            return double.Parse(_inputQueue.Dequeue());
        }
    }

    public static class ConsoleOutputExtension
    {
        private static StringBuilder _builder = new StringBuilder();

        public static void Cout(object o)
        {
            _builder.Append(o);
        }

        public static void CoutF(object o)
        {
            _builder.Append(o);
            Flush();
        }

        public static void Coutln(object o)
        {
            _builder.Append(o);
            _builder.Append('\n');
        }

        public static void Coutln()
        {
            _builder.Append('\n');
        }

        public static void CoutlnF(object o)
        {
            _builder.Append(o);
            _builder.Append('\n');
            Flush();
        }

        public static void Flush()
        {
            Console.Write(_builder.ToString());
            _builder.Clear();
        }
    }

    public static class MathExtension
    {
        //最小公倍数
        public static int LCM(int num1, int num2)
        {
            var gcd = GCD(num1, num2);
            return num1 * (num2 / gcd);
        }

        public static long LCM(long num1, long num2)
        {
            var gcd = GCD(num1, num2);
            return num1 * (num2 / gcd);
        }

        //最大公約数
        public static int GCD(int num1, int num2)
        {
            int a = Math.Max(num1, num2);
            int b = Math.Min(num1, num2);
            int mod;
            while ((mod = a % b) != 0)
            {
                a = b;
                b = mod;
            }

            return b;
        }

        public static long GCD(long num1, long num2)
        {
            long a = Math.Max(num1, num2);
            long b = Math.Min(num1, num2);
            long mod;
            while ((mod = a % b) != 0)
            {
                a = b;
                b = mod;
            }

            return b;
        }
    }

    public static class EnumerableExtension
    {
        public delegate void Function<in T>(T val);

        public static void ForEach<T>(this IEnumerable<T> enumerable, Function<T> function)
        {
            foreach (var x in enumerable)
            {
                function(x);
            }
        }
    }
}