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: Runtime Error)

using System;
using System.Collections.Generic;
using System.Linq;
using static System.Console;
using static System.Math;

class Program
{
    static void Main()
    {
        var NK = ReadLine().Split().Select(int.Parse).ToArray();
        var N = NK[0];
        var K = NK[1];
        if(N*(N-1)/2-K<N-1)
        {
            WriteLine("-1");
            return;
        }
        var u = new int[N * (N - 1) / 2];
        var v = new int[N * (N - 1) / 2];
        var a = 0;
        for (int i = 0; i < N; i++)
        {
            for (int j = i+1; j < N; j++)
            {
                u[a] = i;
                v[a] = j;
                a++;
            }
        }
        var r = new List<int>[N];
        for (int i = 0; i < N; i++)
        {
            r[i] = new List<int>();
        }
        for (int i = 0; i < u.Length; i++)
        {
            r[u[i]].Add(v[i]);
        }

        WriteLine(u.Length - K);
        var c = 0;
        for (int i = 0; i < u.Length-K;)
        {
            if(r[c].Count<=1)
            {
                c++;
                
            }
            else
            {
                var k = r[c][0];
                WriteLine($"{c+1} {k+1}");
                r[c].RemoveAt(0);
                i++;
            }
        }
    }
}