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: Wrong Answer)

import java.util.*;

public class Main {
    public static void main(String[] args) throws Exception {
        
        Scanner sc = new Scanner(System.in);
        
        int N = sc.nextInt();
        int K = sc.nextInt();
        
        int max = (N -1) * (N - 2) / 2;
        
        if ( max < K ) {
            System.out.println(-1);
            return;
        }
        
        Node[] nodes = new Node[N];
        for(int i = 0; i < N; i++){
            nodes[i] = new Node(i);
            
            if (i > 0){
                nodes[0].adjacents.add(nodes[i]);
                nodes[i].adjacents.add(nodes[0]);
            }
        }
        
        int countGoal = max - K;
        int count = 0;

        loop: for(int i = 1; i < N - 1; i++){
            for(int j = i + 1; j < N; j++){
                nodes[i].adjacents.add(nodes[j]);
                nodes[j].adjacents.add(nodes[i]);
                if ( ++count == countGoal ) break loop;
            }
        }
        
        for(int i = 0; i < N - 1; i++){
            for(int j = i + 1; j < N; j++){
                if ( nodes[i].adjacents.contains(nodes[j]) ){
                    System.out.println( (i + 1) + " " + (j + 1) );
                } else {
                    break;
                }
            }
        }
        
    }
    
    static class Node{
        int id;
        
        public Node(int id){
            this.id = id;
        }
        
        List<Node> adjacents = new LinkedList<>();
    }
}