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 Rust (1.42.0) (judge verdict: Wrong Answer)

fn main() {
	let mut s = String::new();
	use std::io::Read;
	std::io::stdin().read_to_string(&mut s).unwrap();
	let mut s = s.split_whitespace();
	let n: usize = s.next().unwrap().parse().unwrap();
	let k: usize = s.next().unwrap().parse().unwrap();
	if k > (n - 1) * (n - 2) / 2 {
		println!("-1");
	} else {
		let mut edge = vec![];
		for i in 2..=n {
			edge.push((1, i));
		}
		let mut left = (n - 1) * (n - 2) / 2 - k;
		if left > 0 {
			'a: for i in 2..n - 1 {
				for j in i + 1..=n {
					edge.push((i, j));
					left -= 1;
					if left == 0 {
						break 'a;
					}
				}
			}
		}
		use std::io::Write;
		let out = std::io::stdout();
		let mut out = std::io::BufWriter::new(out.lock());
		writeln!(out, "{}", edge.len()).unwrap();
		for (a, b) in edge {
			writeln!(out, "{} {}", a, b).unwrap();
		}
	}
}