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 PHP (7.4.4) (judge verdict: Accepted)

<?php
list($n, $k) = ints();
if ($k > ($n - 1) * ($n - 2) / 2) exit('-1');
// 1と他の点を繋ぐ、この時が最短距離2の点の組み合わせは最大となり n-1C2 通り
for ($i = 2; $i <= $n; ++$i) $ans[] =  implode(' ', [1, $i]);
// 減らしたい数だけ直接繋ぐ
$r = ($n - 1) * ($n - 2) / 2 - $k;
for ($i = 2; $i <= $n - 1; ++$i) {
    for ($j = $i + 1; $j <= $n; ++$j) {
        if ($r === 0) break 2;
        $ans[] = implode(' ', [$i, $j]);
        --$r;
    }
}
echo count($ans) . PHP_EOL;
echo implode(PHP_EOL, $ans);
function ints()
{
    return array_map('intval', explode(' ', trim(fgets(STDIN))));
}