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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.*;
import java.util.*;
public class Main{
    public static void main(String[] args) throws IOException{
        MyReader r = new MyReader();        
        int N, K;
        {int[] a = r.ii(); N = a[0]; K = a[1];}
        int k = (N-1)*(N-2)/2;
        if(k < K){
            println(-1);
            return;
        } else{
            int extra = k-K;
            int M = N-1+k-K;
            println(M);
            int n = 1;
            for(int i = 1; i < N; i++){
                println(i+" "+N);
            }
            if(extra == 0)
                return;
            for(int i = 1; i < N-1; i++){
                for(int j = i+1; j < N; j++){
                    println(i+" "+j);
                    extra--;
                    if(extra == 0){
                        return;
                    }
                }
            }
        }
    }
    static void print(Object o){
        System.out.print(o.toString());
    }
    static void println(Object o){
        System.out.println(o.toString());
    }
    static int Int(String s){
        return Integer.parseInt(s);
    }
    static long Long(String s){
        return Long.parseLong(s);
    }
    static class MyReader extends BufferedReader{
        MyReader(){
            super(new InputStreamReader(System.in));
        }
        String s() throws IOException{
            return readLine();
        }
        String[] ss() throws IOException{
            return s().split(" ");
        }
        int i() throws IOException{
            return Int(s());
        }
        int[] ii() throws IOException{
            String[] ss = ss();
            int size = ss.length;
            int[] ii = new int[size];
            for(int j = 0; j < size; j++) ii[j] = Integer.parseInt(ss[j]);
            return ii;
        }
        long l() throws IOException{
            return Long(s());
        }
        long[] ll() throws IOException{
            String[] ss = ss();
            int size = ss.length;
            long[] ll = new long[size];
            for(int j = 0; j < size; j++) ll[j] = Long.parseLong(ss[j]);            
            return ll;
        }
    }
}