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;

class Program
{
    public struct Connection
    {
        public List<int> list;
        public Connection(int index)
        {
            list = new List<int>();
        }
    }

    static void Main(string[] args)
    {
        var line = Console.ReadLine().Split(' ').Select(x => Int32.Parse(x)).ToArray();
        var N = line[0];
        var K = line[1];
        if (((N-1)*(N-2))/2 < K)
        {
            Console.WriteLine(-1);
        }
        else
        {
            var connections = new Connection[N];
            for (int i = 0; i < N; ++i)
            {
                connections[i] = new Connection(i);
            }
            var count = N - K - 1;
            //1
            for (int i = 0; i < count; ++i)
            {
                connections[0].list.Add(i + 2);
            }
            //2
            for (int i = 0; i < K; ++i)
            {
                connections[1].list.Add(i + count + 2);
            }
            Console.WriteLine(count + K);
            foreach (var l in connections[0].list)
            {
                Console.WriteLine($"1 {l}");
            }
            foreach (var l in connections[1].list)
            {
                Console.WriteLine($"2 {l}");
            }
        }
    }
}