Problem:
Score: 500 points

Problem Statement

Does there exist an undirected graph with N vertices satisfying the following conditions?

The graph is simple and connected.

The vertices are numbered 1, 2, ..., N.

Let M be the number of edges in the graph. The edges are numbered 1, 2, ..., M, the length of each edge is 1, and Edge i connects Vertex u_i and Vertex v_i.

There are exactly K pairs of vertices (i,\ j)\ (i < j) such that the shortest distance between them is 2.

If there exists such a graph, construct an example.

Constraints

All values in input are integers.

2 \leq N \leq 100

0 \leq K \leq \frac{N(N - 1)}{2}

Input

Input is given from Standard Input in the following format:

N K

Output

If there does not exist an undirected graph with N vertices satisfying the conditions, print -1.

If there exists such a graph, print an example in the following format (refer to Problem Statement for what the symbols stand for):

M
u_1 v_1
:
u_M v_M

If there exist multiple graphs satisfying the conditions, any of them will be accepted.

Sample Input 1

5 3

Sample Output 1

5
4 3
1 2
3 1
4 5
2 3

This graph has three pairs of vertices such that the shortest distance between them is 2: (1,\ 4), (2,\ 4), and (3,\ 5). Thus, the condition is satisfied.

Sample Input 2

5 8

Sample Output 2

-1

There is no graph satisfying the conditions.

Solution in C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.IO;
using System.Collections.Generic;
using System.Globalization;
using System.Linq;
using System.Text;
using E = System.Linq.Enumerable;

partial class Solver
{
    public void Run()
    {
        var N = ni();
        var K = ni();
        var edges = new List<Tuple<int, int>>();

        var currentK = 0;

        edges.Add(Tuple.Create(0, 1));

        int targetVertex = 0;
        int targetVertexDegree = 1;

        for (int i = 2; i < N; i++)
        {
            var rem = K - currentK - (N - 1 - i);
            if (targetVertexDegree <= rem)
            {
                edges.Add(Tuple.Create(targetVertex, i));
                currentK += targetVertexDegree;
                targetVertexDegree++;
            }
            else
            {
                targetVertex++;
                targetVertexDegree = 1;
                currentK++;
                edges.Add(Tuple.Create(targetVertex, i));
                if (targetVertex == i)
                {
                    currentK = -1;
                    break;
                }
            }
        }

        if (currentK != K)
        {
            cout.WriteLine("-1");
        }
        else
        {
            cout.WriteLine(edges.Count);
            foreach (var e in edges)
            {
                cout.WriteLine("{0} {1}", e.Item1 + 1, e.Item2 + 1);
            }
        }
    }
}

// PREWRITEN CODE BEGINS FROM HERE
partial class Solver : Scanner
{
    public static void Main(string[] args)
    {
#if LOCAL
        new Solver(Console.In, Console.Out).Run();
#else
        Console.SetOut(new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false });
        new Solver(Console.In, Console.Out).Run();
        Console.Out.Flush();
#endif
    }

#pragma warning disable IDE0052
    private readonly TextReader cin;
    private readonly TextWriter cout;
#pragma warning restore IDE0052

    public Solver(TextReader reader, TextWriter writer)
        : base(reader)
    {
        this.cin = reader;
        this.cout = writer;
    }
    public Solver(string input, TextWriter writer)
        : this(new StringReader(input), writer)
    {
    }

#pragma warning disable IDE1006
#pragma warning disable IDE0051
    private int ni() { return NextInt(); }
    private int[] ni(int n) { return NextIntArray(n); }
    private long nl() { return NextLong(); }
    private long[] nl(int n) { return NextLongArray(n); }
    private double nd() { return NextDouble(); }
    private double[] nd(int n) { return NextDoubleArray(n); }
    private string ns() { return Next(); }
    private string[] ns(int n) { return NextArray(n); }
#pragma warning restore IDE1006
#pragma warning restore IDE0051
}

public static class LinqPadExtension
{
    static public T Dump<T>(this T obj)
    {
#if LOCAL
        return LINQPad.Extensions.Dump(obj);
#else
        return obj;
#endif
    }
}
public class Scanner
{
    private readonly TextReader Reader;
    private readonly Queue<string> TokenQueue = new Queue<string>();
    private readonly CultureInfo ci = CultureInfo.InvariantCulture;

    public Scanner()
        : this(Console.In)
    {
    }

    public Scanner(TextReader reader)
    {
        this.Reader = reader;
    }

    public int NextInt() { return int.Parse(Next(), ci); }
    public long NextLong() { return long.Parse(Next(), ci); }
    public double NextDouble() { return double.Parse(Next(), ci); }
    public string[] NextArray(int size)
    {
        var array = new string[size];
        for (int i = 0; i < size; i++) array[i] = Next();
        return array;
    }
    public int[] NextIntArray(int size)
    {
        var array = new int[size];
        for (int i = 0; i < size; i++) array[i] = NextInt();
        return array;
    }

    public long[] NextLongArray(int size)
    {
        var array = new long[size];
        for (int i = 0; i < size; i++) array[i] = NextLong();
        return array;
    }

    public double[] NextDoubleArray(int size)
    {
        var array = new double[size];
        for (int i = 0; i < size; i++) array[i] = NextDouble();
        return array;
    }

    public string Next()
    {
        if (TokenQueue.Count == 0)
        {
            if (!StockTokens()) throw new InvalidOperationException();
        }
        return TokenQueue.Dequeue();
    }

    public bool HasNext()
    {
        if (TokenQueue.Count > 0)
            return true;
        return StockTokens();
    }
    static readonly char[] _separator = new[] { ' ' };
    private bool StockTokens()
    {
        while (true)
        {
            var line = Reader.ReadLine();
            if (line == null) return false;
            var tokens = line.Split(_separator, StringSplitOptions.RemoveEmptyEntries);
            if (tokens.Length == 0) continue;
            foreach (var token in tokens)
                TokenQueue.Enqueue(token);
            return true;
        }
    }
}