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 PyPy3 (2.4.0) (judge verdict: Wrong Answer)

import math


def main():
  n, k = map(int, input().split())

  if n < 3:
    print(-1)
    return

  v = math.factorial(n - 1) // math.factorial(n - 3) // 2

  if k > v:
    print(-1)
    return

  nodes = [(0, i) for i in range(1, n)]
  s = 1
  d = 2

  while v > k:
    nodes.append((s, d))
    d += 1
    v -= 1

    if d == n:
      s += 1
      d = s + 1

  print(len(nodes))

  for s, d in nodes:
    print(s + 1, d + 1)


if __name__ == '__main__':
  main()