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.Generic;
using System.Linq;

public class S
{

    private const long DP_INIT_MINUS1 = -1;
    private const double DP_INIT_DOUBLE_MINUS1 = -1.0;
	private const long MOD = 1000000007;


    public static void Main()
	{
		/*
        var input = Array.ConvertAll(Console.ReadLine().Split(' '), long.Parse);
        var N = input[0];
        var M = input[1];
        */

        var input = Array.ConvertAll(Console.ReadLine().Split(' '), int.Parse);
        var N = input[0];
        var K = input[1];
        /*
            ABC 131 E FriendShips

            解説ACの民。
            確かにスター形にすれば距離2を最大数作れるのは分かるんだけど、
            そこからどう数を「削る」かが分からなかった。
            
            辺数は指定されてないんだから適当なところは繋げてつぶせば良かったんだね。

            で、実装できますか？　という話だよね。解けないのもだめだけど、解説だけ見て
            分かった気になって本番実装できないのはやばいので書きましょう。
            
        */

        var X = N-1;
        var path = (X*(X-1))/2;
        if(K > path){
            Console.WriteLine(-1);
        }

        var list = new List<String>();

        // 全ノード繋ぐ
        for(int i = 2; i <= N; i++){
            list.Add("1 " + i);
        }

        
        var root = 2;
        var target = 3;

        while(path != K){
            list.Add(root + " " + target);
            path--;
            target++;
            if(target > N){
                root++;
                target = root+1;
            }
        }


        foreach(var tgt in list){
            Console.WriteLine(tgt);
        }



        

    }

}