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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.List;

public class Main {

    public static void main(String[] args) throws NumberFormatException, IOException {
        Stdin stdin = new Stdin();
        int n = stdin.nextInt();
        int k = stdin.nextInt();
        
        int max = (n - 1) * (n - 2) / 2;
        if (max < k) {
            System.out.println(-1);
            System.exit(0);
        }
        
        List<Integer> l = new ArrayList<>();
        List<Integer> r = new ArrayList<>();
        for (int i = 0; i < n - 1; i++) {
            l.add(1);
            r.add(i + 2);
        }
        
        List<Integer> x = new ArrayList<>();
        List<Integer> y = new ArrayList<>();
        for (int i = 2; i <= n; i++) {
            for (int j = i + 1; j <= n; j++) {
                x.add(i);
                y.add(j);
            }
        }
        
        for (int i = 0; i < max - k; i++) {
            l.add(x.get(i));
            r.add(y.get(i));
        }
        
        System.out.println(l.size());
        for (int j = 0; j < l.size(); j++) {
            System.out.printf("%d %d%n", l.get(j), r.get(j));
        }
    }

    private static final class Stdin {
        private BufferedReader stdin;
        private ArrayDeque<String> tokens;
        
        public Stdin() {
            this.stdin = new BufferedReader(new InputStreamReader(System.in));
            this.tokens = new ArrayDeque<>();
        }
        
        public String nextToken() throws IOException {
            if (tokens.isEmpty()) {
                for (String token : stdin.readLine().split(" ")) {
                    tokens.add(token);
                }
            }
            return tokens.poll();
        }
        
        public int nextInt() throws NumberFormatException, IOException {
            return Integer.parseInt(nextToken());
        }
        
        public int nextLong() throws NumberFormatException, IOException {
            return Integer.parseInt(nextToken());
        }
    }
}