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;
using System.Collections.Generic;
using System.Text;
using System.Linq;
using static MyIO;


public class E
{
	public static void Main()
	{
		int N = GetInt();
		int K = GetInt();

		if(N == 2)
		{
			if(K == 0)
			{
				Console.WriteLine(1);
				Console.WriteLine("1 2");
				return;
			}

			Console.WriteLine(-1);
			return;
		}

		int comb = (int)combination((int)(N - 1), 2);
		if(K > comb)
		{
			Console.WriteLine(-1);
			return;
		}

		Console.WriteLine(N - 1 + comb - K);
		for(int i = 2; i <= N; i++)
			Console.WriteLine($"1 {i}");

		int rest = comb - K;
		for(int i = 2; i <= N; i++)
		{
			for(int j = i + 1; j <= N; j++)
			{
				if(rest == 0)
					return;
	
				Console.WriteLine($"{i} {j}");
				rest--;
			}
		}
	}

	private static long combination(long n, long k) 
	{
		long r = 1;
		for(long d = 1; d <= k; d++) 
		{
			r *= n--;
			r /= d;
		}
		return r;
	}
}


public static class MyIO
{
	private static string[] args = null;
	private static int num = -1;
	private static int used = -1;

	private static string getArg()
	{
		if(used == num)
		{
			args = Console.ReadLine().Split(' ');
			num = args.Length;
			used = 0;
		}
		return args[used++];
	}

	public static int GetInt(){ return int.Parse(getArg()); }
	public static long GetLong(){ return long.Parse(getArg()); }
	public static double GetDouble(){ return double.Parse(getArg()); }
	public static string GetString(){ return getArg(); }
}