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;//list用
using System.Text;//StringBuilder用
using System.Collections;
using System.Linq;
class Program
{
    static List<int> A = new List<int>();
      static List<int> B = new List<int>();
    static decimal result;
static Hashtable ht=new Hashtable();
static StringBuilder sb = new StringBuilder();
static int N,M,K;
static long[,] table;
    static void Main()
    {
Read4();
//１を中心にしたウニ型をベースに考える。
//1以外の各点から各点の距離は２。これ(N-1個から２点取る)が組み合わせ数最大の形。Kがこれ以上ならムリ。
if((N-1)*(N-2)/2<K){Console.WriteLine("-1");return; }
//ここに一本ずつ線を入れる。線を入れると両者間の距離が１になって一組消える。
M=(N-1)*(N-2)/2-K;//消すべき数量(=線の数)はウニで出来る組み合わせとKとの差異。
Console.WriteLine((M + N-1).ToString()); 
            for(int i=2;i<=N;i++){
Console.WriteLine("1 " + i.ToString());     //ウニを描く
      }
//どの組み合わせでもいいので，とりあえず先頭から消していく。
for(int i=2;i<N;i++){
for(int j=i+1;j<=N;j++){
Console.WriteLine(i.ToString() + " " + j.ToString());
M--;
if(M==0){return;}//線の本数が足りたら完成。
}
}      
    }
  
    static void Read4()//NK１行
    {
        string[] tmp = Console.ReadLine().Split(' ');
       N = int.Parse(tmp[0]);
       K = int.Parse(tmp[1]);
    }


}