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)

// Try AtCoder
// author: Leonardone @ NEETSDKASU

fn main() {
    let mut stdin = String::new();
    std::io::Read::read_to_string(
        &mut std::io::stdin(),
        &mut stdin).unwrap();
    let mut stdin = stdin.split_whitespace();
    let mut get = || stdin.next().unwrap();
    macro_rules! get {
        ($t:ty) => (get().parse::<$t>().unwrap());
        () => (get!(i64));
    }
    
    let n = get!(usize);
    let k = get!();
    let mut joined = vec![vec![false; n]; n];
    let mut cnt = 0;
    for _ in 0 .. k {
        let mut ok = false;
        for i in 0 .. n {
            for j in i+1 .. n {
                for e in j+1 .. n {
                if !joined[i][e] && !joined[j][e] {
                    joined[i][e] = true;
                    joined[e][i] = true;
                    joined[j][e] = true;
                    joined[e][j] = true;
                    ok = true;
                    cnt += 1;
                    break;
                }
                }
                if ok {
                    break;
                }
            }
            if ok {
                break;
            }
        }
    }
    if cnt != k {
        println!("-1");
        return;
    }
    let mut edge = vec![];
    for i in 0 .. n {
        for j in i+1 .. n {
            if joined[i][j] {
                edge.push((j+1,i+1));
            }
        }
    }
    println!("{}", edge.len());
    for &(i, j) in edge.iter() {
        println!("{} {}", i, j);
    }
}