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.Text;

namespace ABC131_E___FriendShips
{
    class Program
    {
        static void Main(string[] args)
        {
            Console.WriteLine(solver());
        }
        static string solver()
        {
            var NK = Array.ConvertAll(Console.ReadLine().Split(' '), int.Parse);
            var N = NK[0];
            var K = NK[1];

            if (K > (N - 1) * (N - 2) / 2) return "-1";

            var graph = new StringBuilder();
            graph.AppendLine((N - 1 + ((N - 1) * (N - 2) / 2 - K)).ToString());
            for (int i = 2; i <= N; i++) graph.AppendLine($"1 {i}");

            var counter = 0;
            for (int i = 2; i < N; i++)
            {
                for (int j = i + 1; j <= N; j++)
                {
                    if (K == (N - 1) * (N - 2) / 2 - counter) return graph.ToString().TrimEnd('\r', '\n');
                    graph.AppendLine($"{i} {j}");
                    counter += 1;
                }
            }
            return "";
        }
    }
}