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.ArrayList;
import java.util.List;
import java.util.Scanner;

public class Main {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int k = sc.nextInt();

		// 条件を満たせるかチェック
		int sum = 0;
		for (int i = n-2; i > 0; i--) {
			sum += i;
		}
		if (sum < k) {
			System.out.println(-1);
		}

		List<String> graph = new ArrayList<>();
		// まず最短距離2が最多になるグラフを書く
		for (int i = 2; i <= n; i++) {
			graph.add("2 " + i);
		}
		// この時点で達成していたら終了
		if (sum == k) {
			print(graph);
			return;
		}
		// 最短距離2の組み合わせがk個になるまで要素をつなげていく
		for (int i = 2; i <= n; i++) {
			for (int j = i + 1; j <= n; j++) {
				graph.add(i + " " + j);
				sum--;
				if (sum == k) {
					print(graph);
					return;
				}
			}
		}
	}

	private static void print(List<String> graph) {
		System.out.println(graph.size());
		for (String pear : graph) {
			System.out.println(pear);
		}
	}
}