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.Linq;
using System.Collections.Generic;
using System.Text;
using System.Text.RegularExpressions;
using static System.Console;
using static System.Math;

class Program
{
    static void Main(string[] args)
    {
        int[] NK = ReadLineParseIntArray();
        int N = NK[0];
        int K = NK[1];
        int cmb = Combination(N - 1, 2);
        if(cmb < K)
        {
            WriteLine(-1);
            return;
        }

        WriteLine(N - 1);
        for(int i = 2; i <= N; i++)
        {
            WriteLine($"1 {i}");
        }
        int count = cmb - K;
        for(int i = 2; i < N; i++)
        {
            for(int j = i + 1; j <= N; j++)
            {
                if (count == 0) return;
                WriteLine($"{i} {j}");
                count--;
            }
        }
    }
    static int[] ReadLineParseIntArray() => ReadLine().Split(' ').Select(int.Parse).ToArray();
    static int Combination(int n, int m)
    {
        if (m == 0) return 1;
        return Combination(n, m - 1) * (n - m + 1) / m;
    }
}