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: Accepted)

use std::str::FromStr;
use std::fmt::Debug;
use std::cmp;

#[allow(dead_code)]
fn read_as_vec<T>() -> Vec<T>
where T: FromStr, <T as FromStr>::Err : Debug{
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).unwrap();
    s.trim().split_whitespace().map(|c| T::from_str(c).unwrap()).collect()

}

#[allow(dead_code)]
fn read_as_string() -> String{
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).unwrap();
    s.trim().to_string()
}

fn print_graph(graph: &Vec<Vec<bool>>){
    for i in 0..graph.len(){
        println!("{:?}", graph[i]);
    }
    
}

fn main(){
    let line: Vec<usize> = read_as_vec();
    let (n, k) = (line[0], line[1]);

    let mut graph: Vec<Vec<bool>> = vec![vec![false;n];n];

    for i in 1..n{
        graph[0][i] = true;
        graph[i][0] = true;
    }

    //print_graph(&graph);

    let mut num_of_pairs = (n-1)*(n-2)/2;

    if num_of_pairs < k{
        println!("-1");
        return;
    }

    for i in 1..n{
        for j in i+1..n{
            if num_of_pairs == k{
                break;
            }
            graph[i][j] = true;
            graph[j][i] = true;
            num_of_pairs -= 1;
        }
    }
    //print_graph(&graph);
    println!("{}", n-1 + ((n-1)*(n-2)/2-num_of_pairs));
    for i in 0..n{
        for j in i+1..n{
            if graph[i][j]{
                println!("{} {}", i+1, j+1);
            }
        }
    }
}