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 PHP7 (7.0.15) (judge verdict: Wrong Answer)

<?php
$input = explode(' ', trim(fgets(STDIN)));

$n = (int)$input[0];
$k = (int)$input[1];

if ($k > (int)((($n-1) * ($n-2))/2)) {
	echo '-1';
	exit();
}
if ($n === 2) {
	echo '1' . PHP_EOL;
	echo '1 2';
}


$points = [];
$points[1] = [];
for ($i=2; $i <= $n; $i++) { 
	$points[$i] = [1];
	$points[1][] = $i;
}
$cnt = (int)((($n-1) * ($n-2))/2);
for ($i=2; $i <= $n ; $i++) { 
	for ($j=$i+1; $j <= $n; $j++) { 
		$points[$i][] = $j;
		$cnt -= 1;
		if ($cnt === $k) {
			break 2;
		}
	}
}
// var_dump($points);
$g = [];
for ($i=1; $i <= $n; $i++) { 
	for ($j=$i+1; $j <= $n; $j++) { 
		$g[$i][$j] = false;
	}
}
for ($i=1; $i <= $n; $i++) { 
	foreach ($points[$i] as $p) {
		if ($i < $p && isset($g[$i][$p])) {
			$g[$i][$p] = true;
		}
	}
}

$edge = [];
for ($i=1; $i <= $n; $i++) { 
	for ($j=$i+1; $j <= $n; $j++) { 
		if ($g[$i][$j]) {
			$edge[] = $i . ' ' . $j;
		}
	}
}
echo count($edge) . PHP_EOL;
echo implode(PHP_EOL, $edge);