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: Runtime Error)

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

namespace Sandbox
{
    internal class Program
    {
        private static readonly int MaxNumber = 100001;

        private static readonly List<int>[] XtoY = Enumerable.Range(0, MaxNumber).Select(_ => new List<int>()).ToArray();
        private static readonly List<int>[] YtoX = Enumerable.Range(0, MaxNumber).Select(_ => new List<int>()).ToArray();
        private static readonly bool[] VisitedX = new bool[MaxNumber];
        private static readonly bool[] VisitedY = new bool[MaxNumber];

        private static void Main(string[] args)
        {
            var scanner = new Scanner();
            var n = scanner.GetNextAsInt();
            var maxX = int.MinValue;
            var maxY = int.MinValue;

            for (var i = 0; i < n; i++)
            {
                var xi = scanner.GetNextAsInt();
                var yi = scanner.GetNextAsInt();
                XtoY[xi].Add(yi);
                YtoX[yi].Add(xi);
                maxX = Math.Max(xi, maxX);
                maxY = Math.Max(xi, maxY);
            }

            var result = 0L;
            for (var xx = 1; xx <= maxX; xx++)
            {
                var countX = 0;
                var countY = 0;

                DfsX(xx, ref countX, ref countY);

                result += (long)countX * (long)countY;
            }

            result -= n;

            Console.WriteLine(result);
        }

        private static void DfsX(int x, ref int countX, ref int countY)
        {
            if (VisitedX[x])
            {
                return;
            }

            countX++;
            VisitedX[x] = true;
            foreach (var yy in XtoY[x])
            {
                DfsY(yy, ref countX, ref countY);
            }
        }

        private static void DfsY(int y, ref int countX, ref int countY)
        {
            if (VisitedY[y])
            {
                return;
            }

            countY++;
            VisitedY[y] = true;
            foreach (var xx in YtoX[y])
            {
                DfsX(xx, ref countX, ref countY);
            }
        }

        #region String Scanner

        public class Scanner
        {
            private const char Separator = ' ';
            private readonly StreamReader _Stream = new StreamReader(Console.OpenStandardInput());
            private int _Pos;
            private string[] _Line = new string[0];

            #region get a element

            public string GetNext()
            {
                // ReSharper disable once InvertIf
                if (this._Pos >= this._Line.Length)
                {
                    // ReSharper disable once PossibleNullReferenceException
                    this._Line = this._Stream.ReadLine().Split(Separator);
                    this._Pos = 0;
                }

                return this._Line[this._Pos++];
            }

            public int GetNextAsInt()
            {
                return int.Parse(this.GetNext());
            }

            public long GetNextAsLong()
            {
                return long.Parse(this.GetNext());
            }

            public double GetNextAsDouble()
            {
                return double.Parse(this.GetNext());
            }

            #endregion

            #region get array

            public string[] ToArrayFromNextLine()
            {
                if (this._Pos >= this._Line.Length)
                {
                    // ReSharper disable once PossibleNullReferenceException
                    this._Line = this._Stream.ReadLine().Split(Separator);
                }

                this._Pos = this._Line.Length;
                return this._Line;
            }

            public int[] ToIntArrayFromNextLine()
            {
                return ToIntArray(this.ToArrayFromNextLine());
            }

            public long[] ToLongArrayFromNextLine()
            {
                return ToLongArray(this.ToArrayFromNextLine());
            }

            public double[] ToDoubleArrayFromNextLine()
            {
                return ToDoubleArray(this.ToArrayFromNextLine());
            }

            #endregion

            #region convert array

            private static int[] ToIntArray(string[] array)
            {
                var result = new int[array.Length];
                for (var i = 0; i < array.Length; i++)
                {
                    result[i] = int.Parse(array[i]);
                }

                return result;
            }

            private static long[] ToLongArray(string[] array)
            {
                var result = new long[array.Length];
                for (var i = 0; i < array.Length; i++)
                {
                    result[i] = long.Parse(array[i]);
                }

                return result;
            }

            private static double[] ToDoubleArray(string[] array)
            {
                var result = new double[array.Length];
                for (var i = 0; i < array.Length; i++)
                {
                    result[i] = double.Parse(array[i]);
                }

                return result;
            }

            #endregion
        }

        #endregion
    }
}