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: Runtime Error)

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

path = Array.new(n) {|i| [i+1]}
sum = n - 2
i = 2
n.downto(2) do |j|
    #p [i, j, sum, path]
    break if i == j - 1
    if sum + path[i].size <= k
        sum += path[i].size
        path[i] << j
        path[j-1] = []
    else
        i += 1
        redo
    end
end

if sum != k
    puts -1
    exit
end

puts n - 1
1.upto(n-1) do |i|
    path[i].each {|e| puts "#{i} #{e}"}
end