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.util.LinkedList;
import java.util.Scanner;

class Edge{
	int s, t;
	public Edge(int _s, int _t) {
		s = _s; t = _t;
	}
}
class Main{
	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
		int N = sc.nextInt(), K = sc.nextInt();
		if((N - 1) * (N - 2) < 2 * K) System.out.println(-1);
		else {
			LinkedList<Edge> edges = new LinkedList<Edge>();
			for(int i = 2; i <= N; i++) edges.add(new Edge(1, i));
			int add = (N - 1) * (N - 2) / 2 - K;
			for(int i = 2; i <= N; i++) {
				for(int j = i + 1; j <= N; j++) {
					if(add <= 0) break;
					else {
						edges.add(new Edge(i, j));
						add--;
					}
				}
			}
			System.out.println(edges.size());
			for(Edge e : edges) {
				System.out.println(e.s+" "+e.t);
			}
		}
	}
}