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.Collections.Generic;
using System.Linq;

public static class Combination
{
    public static IEnumerable<IEnumerable<T>> GetCombinations<T>(this IEnumerable<T> elements, int k)
    {
        return k == 0 ? new[] { new T[0] } :
          elements.SelectMany((e, i) =>
            elements.Skip(i + 1).GetCombinations(k - 1).Select(c => (new[] { e }).Concat(c)));
    }
}

public class Solution
{
    public static void Main()
    {
        var vals = Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
        var N = vals[0];
        var K = vals[1];
        var max = (N - 1) * (N - 2) / 2;

        if (K > max)
        {
            Console.WriteLine(-1);
            return;
        }

        var graph = new List<string>();
        var center = 1;
        for (int i = 2; i <= N; i++)
        {
            graph.Add($"{center} {i}");
        }
        var curK = max;
        foreach (var edge in Combination.GetCombinations(Enumerable.Range(2, N - 1), 2))
        {
            if (curK == K)
            {
                break;
            }

            graph.Add(string.Join(" ", edge));
            curK--;
        }
        Console.WriteLine(string.Join(Environment.NewLine, graph));
    }
}