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: Accepted)

n, k = gets.split.map(&:to_i)

# 初期化 全ての頂点を繋いだ状態（片方の頂点からのみ）とする
graph = Array.new(n) { Array.new }
(1...n).each do |i|
  graph[i] += (1..i).to_a
end

# 辺を 1 つずつ外していく、外した頂点同士の距離が 2 となる
# ただし、全ての頂点が 1 と繋がった状態を保つ
graph.each do |r|
  while r.size > 1 && k > 0
    r.pop
    k -= 1
  end
  break if k == 0
end

# 距離が 2 の組み合わせを全て作れた場合
if k == 0
  puts graph.flatten.size
  graph.each_with_index do |r, from|
    r.each do |to|
      puts "#{from + 1} #{to}"
    end
  end
  # 作れなかった場合
else
  puts -1
end