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)

//package practice; 
import java.io.*;
import java.util.*;
import java.util.Stack;
import java.util.regex.Pattern;


public class Main {

	
	public static class FastReader {
		BufferedReader br;
		StringTokenizer st;
		//it reads the data about the specified point and divide the data about it ,it is quite fast
		//than using direct 

		public FastReader() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}

		String next() {
			while (st == null || !st.hasMoreTokens()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (Exception r) {
					r.printStackTrace();
				}
			}
			return st.nextToken();
		}

		int nextInt() {
			return Integer.parseInt(next());//converts string to integer
		}

		double nextDouble() {
			return Double.parseDouble(next());
		}

		long nextLong() {
			return Long.parseLong(next());
		}

		String nextLine() {
			String str = "";
			try {
				str = br.readLine();
			} catch (Exception r) {
				r.printStackTrace();
			}
			return str;
		}
	}
	
	public static PrintWriter out = new PrintWriter (new BufferedOutputStream(System.out));
	static long mod = (long)(1e9+7);
	public static void main(String[] args) {
		 FastReader sc = new FastReader();
		 
		long n = sc.nextLong();
		long k = sc.nextLong();
		long max = ((n-1)*(n-2))/2;
		List<Pair> ans = new ArrayList<>();
		if(k>max) out.println(-1);
		else {
			for(int i=2;i<=n;++i) ans.add(new Pair(1,i));
			long need = max-k;
			for(int i=2;i<=n && need>0;++i) {
				for(int j=i+1;j<=n && need>0;++j) {
					ans.add(new Pair(i,j));
					--need;
				}
			}
			
			out.println(ans.size());
			for(Pair p : ans) out.println(p.u+" "+p.v);
		}
		
		 out.close();
		 
	}
	static class Pair{
		int u;
		int v;
		Pair(int u,int v){
			this.u = u;
			this.v = v;
		}
	}
	
}