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;
namespace I_am_the_green_coder{
    class Inonoa{
        // なんか入力用の関数作ったけどまだテストしてないので使う前に確かめて
        static void Main(){
            string[] nk = Console.ReadLine().Split();
            long n = long.Parse(nk[0]);
            long k = long.Parse(nk[1]);

            List<long[]> hens = new List<long[]>();
            for(long i=1;i<n;i++){
                hens.Add(new long[2]{i,n});
            }
            long count = (n-2)*(n-1) /2;
            if(k>count){
                Console.WriteLine(-1);
                return;
            }else if(k==count){
                Console.WriteLine(n-1);
                foreach(long[] hen in hens){
                    Console.WriteLine(hen[0].ToString() + " " + hen[1].ToString());
                }
                return;
            }

            for(long i=1;i<n;i++){
                for(long j=i+1;j<n+1;j++){
                    hens.Add(new long[2]{i,j});
                    count --;
                    if(count==k){
                        Console.WriteLine(hens.Count);
                        foreach(long[] hen in hens){
                            Console.WriteLine(hen[0].ToString() + " " + hen[1].ToString());
                        }
                        return;
                    }
                }
            }
        }

        static readonly long MOD = 1000000007;

        ///<summary>a_1, a_2, a_3, ...みたいなの</summary>
        static long[] ILongs(){
            string[] s = Console.ReadLine().Split();
            long[] re = new long[s.Length];
            for(long i=0;i<s.Length;i++){
                re[i] = long.Parse(s[i]);
            }
            return re;
        }

        ///<summary>xooxoxoxxoxo...みたいなの</summary>
        static char[] IChars(){
            return Console.ReadLine().ToCharArray();
        }

        ///<summary>n m とかをちょっとはやくかくだけ</summary>
        static string[] IStrings(){
            return Console.ReadLine().Split();
        }

        ///<summary>n行の入力を取ったり</summary>
        static long[][] ILongLongs(long n){
            long[][] re = new long[n][];
            for(long i=0;i<n;i++){
                string[] s = Console.ReadLine().Split();
                re[i] = new long[s.Length];
                for(long j=0;j<s.Length;j++){
                    re[i][j] = long.Parse(s[j]);
                }
            }
            return re;
        }

        static char[][] ICharsChars(long n){
            char[][] re = new char[n][];
            for(long i=0;i<n;i++){
                re[i] = Console.ReadLine().ToCharArray();
            }
            return re;
        }
    }
}