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 Java (OpenJDK 11.0.6) (judge verdict: Wrong Answer)

import java.util.*;

public class Main {
	public static void main(String[] args) {
		Main main = new Main();
		main.run();
	}


	class P{
		int s;
		int t;
		public P(int s, int t) {
			this.s=s;
			this.t=t;
		}
	}
	public void run() {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int k = sc.nextInt();
		ArrayList<P> ans = new ArrayList<>();
		for(int i=0; i<n-1; i++) {
			ans.add(new P(i+1, n));
		}

		ArrayList<P> tmp = new ArrayList<>();
		for(int i=0; i<n-1;i++) {
			for(int j=0; j<i; j++) {
				tmp.add(new P(i+1, j+1));
			}
		}

		int cnt = (n-1)*(n-2)/2;
		if(cnt<k) {
			System.out.println(-1);
			sc.close();
			return;
		}

		for(int i=0; i<tmp.size(); i++) {
			ans.add(tmp.get(i));
			cnt--;
			if(k==cnt) {
				break;
			}
		}

		System.out.println(ans.size());
		for(P p : ans) {
			System.out.println(p.s+" "+p.t);
		}
		sc.close();
	}


}