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 Julia (0.5.0) (judge verdict: Accepted)

parseInt(x) = parse(Int, x)
parseArray(x::Array{SubString{String}, 1}) = map(parseInt, x)

function main()
  N,K = readline() |> split |> parseArray

  b=binomial(N-1,2)
  if K>b
    println(-1)
    return
  end

  M=N-1+(b-K)
  println(M)

  for i in 2:N
    println("1 $i")
  end
  # for i in 2:min(M-N+2,N)
  #   println("$i $(i%N+1)")
  # end
  # for i in 2:min(M-2N+3,N)
  #   println("$i $((i+1)%N+1)")
  # end

  for j in 1:M÷(N-1)+1
    for i in 2:min(M-j*(N-1)+1,N)
      # println("$i $((i+j-1)%N+1)")
      println("$i $(i+j+(i+j>N?-N+1:0))")
    end
  end
end

main()