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 (1.15.1) (judge verdict: Wrong Answer)

use std::cmp::*;
use std::io::*;

fn main() {
    let mut s: String = String::new();
    stdin().read_to_string(&mut s).ok();
    let mut itr = s.trim().split_whitespace();
    let n: usize = itr.next().unwrap().parse().unwrap();
    let k: usize = itr.next().unwrap().parse().unwrap();
    // 任意の2点間の組み合わせ = n * (n - 1) / 2
    // 真ん中の1点と組む組み合わせ = n - 1
    // n * (n - 1) - 2*n+2 / 2
    // (n * n - 3 * n + 2) / 2 = (n - 2) * (n - 1) / 2
    if k > (n - 2) * (n - 1) / 2 {
        println!("-1");
    } else {
        // まず k = (n - 2) * (n - 1) / 2の場合を作る
        let mut ans = Vec::new();
        for i in 2..n + 1 {
            ans.push((1, i));
        }
        let mut iranai = (n - 2) * (n - 1) / 2 - k;
        for i in 2..n + 1 {
            for j in i + 2..n + 1 {
                if iranai == 0 {
                    break;
                }
                ans.push((i, j));
                iranai -= 1;
            }
            if iranai == 0 {
                break;
            }
        }
        // output
        let mut out = Vec::new();
        writeln!(out, "{}", ans.len()).ok();
        for &(a, b) in ans.iter() {
            writeln!(out, "{} {}", a, b).ok();
        }
        stdout().write_all(&out).unwrap();
    }
}