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.*;

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

        if (n * (n - 1) / 2 - (n - 1) < k) {
            System.out.println(-1);
            return;
        }

        ArrayList<String> buf = new ArrayList<String>();
        int num = (n - 2) * (n - 1) / 2;
        for (int i = 1; i < n; ++i) {
            buf.add(String.format("%d %d", 1, i + 1));
        }

        for (int i = 1; i < n; ++i) {
            boolean done = false;
            for (int j = i + 1; j < n; ++j) {
                if (num == k) {
                    done = true;
                    break;
                }
                buf.add(String.format("%d %d", i + 1, j + 1));
                num--;
            }
            if (done) {
                break;
            }
        }

        System.out.println(buf.size());
        for (String b: buf) {
            System.out.println(b);
        }
    }
}