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: Time Limit Exceeded)

// %%
import java.util.*;

// %%
public class Main {

    private static int N;
    private static int K;

    public static void main(String[] args) {
        load();
        solve();
    }

    private static void load() {
        Scanner sc = new Scanner(System.in);
        N = sc.nextInt();
        K = sc.nextInt();
    }

    private static void solve() {
        if (K > (N - 1) * (N - 2) / 2) {
            System.out.println("-1");
            return;
        }

        int cnt = (N - 1) * (N - 2) / 2;
        String rendered = "" + (N - 1 + cnt - K) + "\n";

        for (int i = 2; i <= N; i += 1) {
            rendered += "1 " + i + "\n";
        }

        int from = 2;
        boolean finished = false;
        while (true) {
            int to = from + 1;
            while (to <= N) {
                rendered += from + " " + to + "\n";
                cnt -= 1;
                if (cnt == K) {
                    finished = true;
                    break;
                }
                to += 1;
            }
            if (finished) {
                break;
            }
            from += 1;
        }

        System.out.println(rendered);
    }

}

// %%
// Main.main(new String[0]);