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 Scala (2.11.7) (judge verdict: Wrong Answer)

import java.io._
import java.util.StringTokenizer
import scala.util.control.Breaks.{breakable,break}

object Main extends App {
  val in = new InputReader(System.in)
  val pw = new PrintWriter(System.out)

  // val a = new Array[Int](N)

  val N, K = in.next().toInt

  if (N == 2) {
    if (K == 0) {
      println(1)
      println(1, 2)
    }
    else {
      println(-1)
    }
  }
  else if (N == 3) {
    if (K == 0) {
      println(3)
      println(1, 2)
      println(2, 3)
      println(3, 1)
    }
    else if (K == 1) {
      println(2)
      println(1, 2)
      println(2, 3)
    }
    else
      println(-1)
  }
  else {
    if (K == N) {
      pw.println(N)
      pw.println(N, 1)
      for (i <- 1 until N)
        pw.println(i, i+1)
    }
    else {
      var tmp = ((N-2) * (N-1)) / 2

      if (tmp < K)
        pw.println(-1)
      else {
        var ans: List[(Int, Int)] = Nil

        for (i <- 2 to N) {
          ans = (i, 1) :: ans
        }


        var l = 2
        var r = 3
        while(tmp > K) {
          ans = (l, r) :: ans

          if (r == N) {
            l += 1
            r = l + 1
          }
          else {
            r += 1
          }

          tmp -= 1
        }

        pw.println(ans.length)
        ans.foreach {case (a, b) => pw.println(s"$a $b")}
      }
    }

    pw.flush()
  }
}


class InputReader(stream: InputStream) {
  private val reader = new BufferedReader(new InputStreamReader(stream))
  private var tokenizer: StringTokenizer = new StringTokenizer(reader.readLine())
  def next(): String = {
    while (!tokenizer.hasMoreTokens()) {
      tokenizer = new StringTokenizer(reader.readLine())
    }
    tokenizer.nextToken()
  }
}