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

class TEST{
	static void Main(){
		Sol mySol =new Sol();
		mySol.Solve();
	}
}

class Sol{
	public void Solve(){
		
		if(K > (N - 1) * (N - 2) / 2){
			Console.WriteLine(-1);
			return;
		}
		
		bool[][] a = new bool[N][];
		for(int i=0;i<N;i++){
			a[i] = new bool[N];
		}
		
		for(int i=1;i<N;i++){
			a[0][i] = true;
		}
		int tot = (N - 1) * (N - 2) / 2;
		List<int> L = new List<int>();
		List<int> R = new List<int>();
		bool fin = false;
		for(int i=N-1;i>=1;i--){
			if(fin) break;
			for(int j=N-1;j>i;j--){
				if(fin) break;
				if(tot > K){
					tot--;
					a[i][j] = true;
					continue;
				}
				fin = true;
				for(int ii=0;ii<N;ii++){
					for(int jj=0;jj<N;jj++){
						if(a[ii][jj]){
							L.Add(ii + 1);
							R.Add(jj + 1);
						}
					}
				}
				break;
				
			}
		}
		
		Console.WriteLine(L.Count);
		for(int i=0;i<L.Count;i++){
			Console.WriteLine("{0} {1}",L[i], R[i]);
		}
		
		
	}
	int N,K;
	public Sol(){
		var d = ria();
		N = d[0]; K = d[1];
	}

	static String rs(){return Console.ReadLine();}
	static int ri(){return int.Parse(Console.ReadLine());}
	static long rl(){return long.Parse(Console.ReadLine());}
	static double rd(){return double.Parse(Console.ReadLine());}
	static String[] rsa(char sep=' '){return Console.ReadLine().Split(sep);}
	static int[] ria(char sep=' '){return Array.ConvertAll(Console.ReadLine().Split(sep),e=>int.Parse(e));}
	static long[] rla(char sep=' '){return Array.ConvertAll(Console.ReadLine().Split(sep),e=>long.Parse(e));}
	static double[] rda(char sep=' '){return Array.ConvertAll(Console.ReadLine().Split(sep),e=>double.Parse(e));}
}