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;

namespace ConsoleApp
{
    class Program
    {
        static void Main(string[] args)
        {
            var ss = Console.ReadLine().Split();
            var N = int.Parse(ss[0]);
            var K = int.Parse(ss[1]);

            var sum = 0;
            for (int i = N - 2; i > 0; i--)
            {
                sum += i;
            }

            if (sum < K)
            {
                Console.WriteLine(-1);
                return;
            }

            var edgeList = new List<string>();
            var edgeNum = 0;

            edgeList.Add("1 2");
            edgeNum++;

            for (int i = 3; i <= N; i++)
            {
                edgeList.Add("2 " + i);
                edgeNum++;
            }

            if (sum == K)
            {
                ShowAns(edgeNum, edgeList);
                return;
            }

            var diff = sum - K;
            for (int i = 3; i <= N; i++)
            {
                edgeList.Add("1 " + i);
                edgeNum++;

                diff--;
                if (diff == 0)
                {
                    ShowAns(edgeNum, edgeList);
                    return;
                }
            }

            for (int i = 3; i < N; i++)
            {
                for (int j = i; j <= N; j++)
                {
                    edgeList.Add(i + " " + j);
                    edgeNum++;

                    diff--;
                    if (diff == 0)
                    {
                        ShowAns(edgeNum, edgeList);
                        return;
                    }
                }
            }
        }

        static void ShowAns(int edgeNum, List<string> edge)
        {
            Console.WriteLine(edgeNum);
            foreach (var item in edge)
            {
                Console.WriteLine(item);
            }
        }
    }
}