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.Scanner;

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

        // 作れる最大値
        int max = n - 2;
        if (n >= 3) {
            max += (n - 3) * (n - 2) / 2;
        }
        if (max < k) {
            // 可能より多く作らなくてはならない
            System.out.println(-1);
            return;
        }
        int del = k - max;
        int path = n - 1 - del;
        System.out.println(path);
        p(1, 2);
        for (int i = 3; i <= n; i++) {
            // 先にpathを構成して消していく
            p(2, i);
        }
        int count = 0;
        for (int i = 3; i <= n; i++) {
            for (int j = i + 1; j <= n; j++) {
                p(i, j);
                count++;
                if (count == -del) {
                    return;
                }
            }
        }
        for (int i = 3; i < n; i++) {
            p(1, i);
            count++;
            if (count == -del) {
                return;
            }
        }
    }

    static void p(int a, int b) {
        System.out.println(a + " " + b);
    }
}