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 JavaScript (node.js v5.12) (judge verdict: Runtime Error)

((input) => {
  const data = input.split('\n')[0].split(' ');
  // ノードの数
  const N = +data[0];
  // 最短距離が2になるノードの組み合わせの数
  const K = +data[1];

  // console.log(`N = ${N}`);
  // console.log(`K <= ${(N - 2) * (N - 1) / 2}`);

  if (N <= 2) {
    console.log('-1');
    return;
  }

  const max = (N - 2) * (N - 1) / 2;

  if (N > max) {
    console.log('-1');
    return;
  }

  // 1が真ん中で1と他のノードを全て繋ぐ
  const edges = Array(N - 1)
    .fill(null)
    .map((_, i) => [1, i + 2])
    .concat(
      Array(max - K)
        .fill(null)
        .reduce((r, _, i) => [
          r[0].concat([[r[1], r[1] - i - 1 - r[2]]]),
          r[1] - i - 1 - r[2] > 2 ? r[1] : r[1] - 1,
          r[1] - i - 1 - r[2] > 2 ? r[2] : r[2] - r[1] + 2
        ], [[], N, 0])
        [0]
    );

  console.log(`${edges.length}\n${edges.map(edge => edge.join(' ')).join('\n')}`);
})(
  require("fs").readFileSync("/dev/stdin", "utf8")
);