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# (.NET Core 3.1.201) (judge verdict: Wrong Answer)

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

namespace atcoder
{
    class Program
    {
        static void Main(string[] args)
        {
            var input = Console.ReadLine();
            var list = input.Split(" ");
            int n = Int32.Parse(list[0]), k = Int32.Parse(list[1]);

            var nc2 = (n - 1) * (n - 2) / 2; 

            if (k > nc2)
            {
                Console.WriteLine(-1);
                return;
            }

            var ret = new List < (int x, int y) > ();

            int index = 0;
            for (var i = 1; i <= n; i++)
            {
                for (var j = i + 1; j <= n; j++)
                {
                    ret.Add((i, j));
                    if(i>1)index++;
                    if (index >= nc2 - k)break;
                }
                if (index >= nc2 - k)break;
            }

            Console.WriteLine(ret.Count);
            foreach (var r in ret)
            {
                Console.WriteLine(String.Format("{0} {1}", r.x, r.y));
            }
        }
    }
}