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: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace ABC131
{
    class E
    {
        static void Main(string[] args)
        {

            int[] a = Console.ReadLine().Split(' ').Select(v => int.Parse(v)).ToArray();
            int N = a[0], K = a[1];

            int max = (N - 1) * (N - 2) / 2;


            if (K <= max)
            {

                List<int[]> edges = new List<int[]>();
                for (int i = 0; i < N - 1; i++)
                {
                    int[] e = { 1, i + 2 };
                    edges.Add(e);
                }

                List<int[]> noEdges = new List<int[]>();
                for (int i = 2; i < N; i++)
                {
                    for (int j = i + 1; j <= N; j++)
                    {
                        int[] e = { i, j };
                        noEdges.Add(e);
                    }
                }

                for (int i = 0; i < max - K; i++)
                {
                    int[] e = noEdges[i];
                    edges.Add(e);
                }

                Console.WriteLine(edges.Count);
                foreach(int[] e in edges)
                {
                    Console.WriteLine(e[0] + " " + e[1]);
                } 

            }
            else
            {
                Console.WriteLine(-1);
            }
        } 

    }
}