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.*;
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 == 1 && k == 0) {
            System.out.println(0);
            return;
        }
        if(n == 2 && k == 0) {
            System.out.println(1);
            System.out.println(1 + " " + 2);
            return;
        }
        if(n >= 4) {
            if(n == k) {
                int src = 1;
                int dest = 2;
                System.out.println(n);
                for(int i = 0; i < n-1; i++) {
                    System.out.println(src + " " + dest);
                    src++;
                    dest++;
                }
                System.out.println(n + " " + 1);
                return;
            }
            if(n == k + 1) {
                int src = 1;
                int dest = 2;
                System.out.println(n+1);
                for(int i = 0; i < n-1; i++) {
                    System.out.println(src + " " + dest);
                    src++;
                    dest++;
                }
                System.out.println(n + " " + 1);
                System.out.println(1 + " " + 3);
                return;
            }
        }
        if(n - 2 < k) {
            System.out.println(-1);
            return;
        }
        int m = n - 1;
        System.out.println(m);
        int src = 1;
        int dest = 2;
        for(int i = 0; i < m - k; i++) {
            System.out.println(src + " " + dest);
            dest++;
        }
        src = dest - 1;
        for(int i = m - k; i < m; i++) {
            System.out.println(src + " " + dest);
            dest++;
        }
    }
}