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.Generic;
class Program
{
	static void Main(string[] args)
	{
		string[] str = Console.ReadLine().Split();
		int N = int.Parse(str[0]);
		int K = int.Parse(str[1]);
		bool flag = true;
		if(K>N*(N-1)/2-(N-1)){
			flag = false;
		}
		var ans = new List<int[]>();
		if(flag){
			for(var i=2;i<=N;i++){
				ans.Add(new int[2]{1,i});
			}
			long ct = (N*(N-1)/2-(N-1))-K;
			while(ct>0){
				for(var i=2;i<=N-1;i++){
					if(ct==0){
						break;
					}
					for(var j=i+1;j<=N;j++){
						ans.Add(new int[2]{i,j});
						ct--;
						if(ct==0){
							break;
						}
					}
				}
			}
			Console.WriteLine(ans.Count);
			for(var i=0;i<ans.Count;i++){
				Console.WriteLine(ans[i][0]+" "+ans[i][1]);
			}
		} else {
			Console.WriteLine("-1");
		}
	}
}