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)

#[allow(unused_macros)]
macro_rules! invec {
    ( $t:ty ) => {{
        let mut s = String::new();
        match std::io::stdin().read_line(&mut s) {
            Ok(0) => Vec::<$t>::new(),
            Ok(n) => s.trim().split_whitespace().map(|s| s.parse::<$t>().unwrap()).collect::<Vec<$t>>(),
            Err(_) => Vec::<$t>::new(),
        }
    }}
}

#[allow(unused_macros)]
macro_rules! input {
    ( $($t:ty),* ) => {{
        let mut s = String::new();
        std::io::stdin().read_line(&mut s);
        let mut splits = s.trim().split_whitespace();
        ($(
            {
                 splits.next().unwrap().parse::<$t>().unwrap()
            },
        )*)
    }}
}

struct Combinations<T: Copy, R: Copy> {
    a: Vec<T>,
    b: Vec<R>,
    a_counter: usize,
    b_counter: usize,
}

impl<T: Copy, R: Copy> Combinations<T, R> {
    fn new(a: Vec<T>, b: Vec<R>) -> Combinations<T, R> {
        Combinations { a: a, b: b, a_counter: 0, b_counter: 0 }
    }
}

impl<T: Copy, R: Copy> Iterator for Combinations<T, R> {
    type Item = (T, R);

    fn next(&mut self) -> Option<Self::Item> {
        if self.a_counter >= self.a.len() {
            return None;
        }

        let val = Some((self.a[self.a_counter], self.b[self.b_counter]));
        if self.b_counter + 1 < self.b.len() {
            self.b_counter += 1;
        } else {
            self.a_counter += 1;
            self.b_counter = 0;
        }
        return val;
    }
}

#[allow(unused_must_use)]
#[allow(unused_variables)]
fn solve() {
    let (n, k) = input!(usize, usize);
    let arr = invec!(i64);

    let max = (n-1) * (n-2) / 2;

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

    let add = max - k;
    let mut edge = Vec::with_capacity(n - 1 + add);
    for i in 1..n {
        edge.push((i, n));
    }

    println!("max = {} , add = {}", max, add);
    edge.append(&mut Combinations::new((1..n).collect(), (1..n).collect())
                    .filter(|&(a, b)| a < b)
                    .take(add)
                    .collect());
    
    println!("{}", edge.len());

    for val in edge {
        println!("{} {}", val.0, val.1);
    }
}

fn main() {
    solve();
}