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 (1.42.0) (judge verdict: Accepted)

use proconio::{input, fastout};

fn answer(links: std::vec::Vec<std::vec::Vec<bool>>, n: usize) {
    for i in 0..n {
        for j in (i+1)..n {
            if links[i][j] {
                println!("{} {}", i+1, j+1);
            }
        }
    }
}

fn main() {
    input!{
        (n, k): (usize, usize)
    };

    let mut cnt = (n-1) * (n-2) / 2;
    let mut m = 0;
    if k>cnt {
        println!("-1");
        return;
    }

    let mut links = vec![vec![false; n]; n];
    for j in 0..(n-1) {
        m += 1;
        links[n-1][j] = true;
        links[j][n-1] = true;
    }

    'all: for i in 0..(n-1) {
        for j in (i+1)..(n-1) {
            if cnt==k {
                break 'all;
            } else {
                links[i][j] = true;
                links[j][i] = true;
                cnt -= 1;
                m += 1;
            }
        }
    }

    println!("{}", m);
    answer(links, n);
}