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 = gets.split.map(&:to_i)
if n[1] == 2
  puts "-1"
  exit
end
friend  = 0
side = []
for i in 2..n[0]
  side.push([1,i])
end
(n[0]-2).downto(1){|i| friend += i}
if friend < n[1]
  puts "-1"
  exit
end
count = 1
check = 2
while friend > n[1]
  friend -= 1
  if check + count <= n[0]
    side.push([check,check+count])
    check += 1
  else
    check = 2
    count += 1
  end
  if count > n[0]
    puts "-1"
    exit
  end
end

puts side.length
(side.length).times{|i| puts side[i].join(" ")}