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 Common Lisp (SBCL 1.1.14) (judge verdict: Wrong Answer)

(let ((n (read))
      (k (read))
      (ans (list)))
  (if (> k (floor (* (1- n) (- n 2)) 2))
      (princ -1)
      (progn (dotimes (i (1- n))
               (setf ans (append ans (list (1+ i) n))))
             (princ ans)
             (loop for i from 1 upto (1- n) while (> k 0) do
                   (loop for j from (1+ i) upto (1- n) while (> k 0) do
                         (setf ans (append ans (list i j)))
                         (decf k)))
             (format t "~a~%~{~a ~a~%~}" (floor (length ans) 2) ans))))