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 Ruby (2.3.3) (judge verdict: Wrong Answer)

N, K = gets.split.map(&:to_i)
if N == 2 || (K > N - 2)
  puts "-1"
  exit(0)
elsif K > 0
  ans = []
  t = 0
  ans << [1, 2]
  i = 3
  while t < K
    ans << [2, i]
    ((i + 1)..(K + 2)).each do |j|
      ans << [i, j]
    end
    t += 1
    i += 1
  end
  (i..N).each do |j|
    (1..N).each do |k|
      break if j == k
      ans << [j, k]
    end
  end
  puts ans.size
  ans.each do |e|
    puts "#{e[0]} #{e[1]}"
  end
else
  ans = []
  (1..N).each do |j|
    (1..N).each do |k|
      break if j == k
      ans << [j, k]
    end
  end
  puts ans.size
  ans.each do |e|
    puts "#{e[0]} #{e[1]}"
  end
end