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;

namespace atCoder
{
    class Program
    {
        static void Main(string[] args)
        {
            var input = Console.ReadLine().Split(' ');
            int vert = int.Parse(input[0]);
            int con2 = int.Parse(input[1]);

            int maxcon = vert * (vert - 1) / 2;
            if(con2 > maxcon / 2)
                Console.WriteLine("-1");
            else
            {
                int cutcount = 0;
                for(int n=0;n< vert; n++)
                {
                    bool cut = false;
                    for (int m = n; m < vert; m++)
                    {
                        if (n == m)
                            continue;
                        if (cutcount < con2 && (cut == false || (n==0 && m == vert -1)))
                        {
                            cutcount++;
                            cut = true;
                            continue;
                        }

                        Console.WriteLine(string.Format("{0} {1}", n+1, m+1));

                    }
                }

            }

        }

    }
}