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;
using static System.Console;
using static System.Math;

class MainClass
{
    static int N, K;
    static void Main()
    {
        var NK = ReadLine().Split().Select(int.Parse).ToArray();
        N = NK[0];K = NK[1];
        var max = (int)Modular.Ncr(N - 1, 2);
        if (K > max) { WriteLine(-1);return; }
        int d = max - K;
        WriteLine(d + N-1);
        for (int i = 2; i <= N; i++)
        {
            WriteLine($"1 {i}");
        }
        int num = 0;
        
        for (int i = 2; i <=N-1; i++)
        {
            for (int j = i+1 ; j <= N; j++)
            {
                num++;
                WriteLine($"{i} {j}");
                if (num == d) return;
            }
        }
    }
}
class Modular
{
    private const int M = 1000000007;
    private long value;
    public Modular(long value = 0) { this.value = value; }
    public static implicit operator Modular(long a)
    {
        var m = a % M;
        return new Modular((m < 0) ? m + M : m);
    }
    public static Modular operator +(Modular a, Modular b)
    => a.value + b.value;
    public static Modular operator -(Modular a, Modular b)
    => a.value - b.value;
    public static Modular operator *(Modular a, Modular b)
    => a.value * b.value;
    public static Modular Pow(Modular a, int n)
    {
        switch (n)
        {
            case 0:
                return 1;
            case 1:
                return a;
            default:
                var p = Pow(a, n / 2);
                return p * p * Pow(a, n % 2);
        }
    }
    public static Modular operator /(Modular a, Modular b)
    {
        return a * Pow(b, M - 2);
    }
    private static readonly List<int> facs = new List<int> { 1 };
    public static Modular Fac(int n)   //階乗
    {
        for (int i = facs.Count; i <= n; ++i)
        {
            facs.Add((int)(Math.BigMul(facs.Last(), i) % M));
        }
        return facs[n];
    }
    public static Modular Fac(int r, int n)
    {
        int temp = 1;
        for (int i = r; i <= n; i++)
        {
            temp = (int)(Math.BigMul(temp, i) % M);
        }
        return temp;
    }
    public static Modular Ncr(int n, int r) //nCr
    {
        return (n < r) ? 0
             : (n == r) ? 1
                        : (n < 1000000) ? Fac(n) / (Fac(r) * Fac(n - r))
                            : Fac(n - r + 1, n) / Fac(r);
    }
    public static explicit operator int(Modular a)
    {
        return (int)a.value;
    }
}