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.Linq;
using System.Collections.Generic;
class c
{
    static void Main()
    {
        var inp = Array.ConvertAll(Console.ReadLine().Split(), int.Parse);
        int n = inp[0], k = inp[1];
        if (k > n * (n - 1) / 2 - n) Console.WriteLine(-1);
        else
        {
            var circle = new List<Tuple<int, int>>();
            var inside = new List<Tuple<int, int>>();
            for (int i = 1; i < n; i++)
            {
                circle.Add(new Tuple<int, int>(i, i + 1));
            }
            circle.Add(new Tuple<int, int>(1, n));
            for (int i = 1; i <= n; i++)
            {
                for (int j = i + 1; j <= n; j++)
                {
                    inside.Add(new Tuple<int, int>(i, j));
                }
            }
            for (int i = 0; i < circle.Count(); i++)
            {
                inside.Remove(circle[i]);
            }
            Console.WriteLine(n * (n - 1) / 2 - k);
            for (int i = 0; i < circle.Count(); i++)
            {
                Console.WriteLine("{0} {1}", circle[i].Item1, circle[i].Item2);
            }
            for (int i = 0; i < inside.Count() - k; i++)
            {
                Console.WriteLine("{0} {1}", inside[i].Item1, inside[i].Item2);
            }
        }
    }
}