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)

require 'pp'
N, K = gets.chomp.split(" ").map(&:to_i)
conn = Array.new(N){Array.new(N, false)}
conn[0][1] = true
conn[1][0] = true

if K > N * (N - 1) / 2 - (N - 1)
    puts -1
    exit
end

for j in 1..N-1
    conn[0][j] = true
end

d1 = (N * (N - 1) / 2 - (N - 1)) - K
for i in 1..N-2
    break if d1 == 0
    for j in i+1..N-1
        break if d1 == 0
        conn[i][j] = true
        d1 -= 1
    end
end

puts conn.flatten.count(true)
for i in 0..N-2
    for j in i+1..N-1
        if conn[i][j]
            puts "#{i+1} #{j+1}"
        end
    end
end