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)

fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>()
        .split_whitespace()
        .map(|e| e.parse().ok().unwrap())
        .collect()
}

#[allow(dead_code)]
fn read_vec2<T: std::str::FromStr>(n: u32) -> Vec<Vec<T>> {
    (0..n).map(|_| read_vec()).collect()
}


fn makestr(n: u32, k: u32, m: u32, sub: u32) -> String {
    let mut s = String::new();
    s += &format!("{}\n", m);
    for i in 0..n-1 {
        s += &format!("1 {}\n", i + 2);
    }

    for j in 0..sub {
        let l = j + 2;
        s += &format!("{} {}\n", l, l + 1);
    }

    return s;
}

fn solve(n: u32, k: u32) -> Option<String> {
    if n <= 2 || ((n - 1) * (n - 2) / 2) < k {
        return None;
    } else if n == 3 {
        if k == 1 {
            return Some("2\n1 2\n2 3".to_string());
        } else {
            return None;
        }
    } else {
        let c = (n - 1) * (n - 2) / 2;
        let sub = c - k;
        let m = n - 1 + sub;
        return Some(makestr(n, k, m, sub));
    }
}

fn main() {
    let v = read_vec::<u32>();
    let n = v[0];
    let k = v[1];

    match solve(n, k) {
        None => println!("-1"),
        Some(s) => println!("{}", s),
    };
}