Problem:
Score : 700 points

Problem Statement

Given are positive integers N and K.

Determine if the 3N integers K, K+1, ..., K+3N-1 can be partitioned into N triples (a_1,b_1,c_1), ..., (a_N,b_N,c_N) so that the condition below is satisfied. Any of the integers K, K+1, ..., K+3N-1 must appear in exactly one of those triples.

For every integer i from 1 to N, a_i + b_i \leq c_i holds.

If the answer is yes, construct one such partition.

Constraints

1 \leq N \leq 10^5

1 \leq K \leq 10^9

Input

Input is given from Standard Input in the following format:

N K

Output

If it is impossible to partition the integers satisfying the condition, print -1. If it is possible, print N triples in the following format:

a_1 b_1 c_1
:
a_N b_N c_N

Sample Input 1

1 1

Sample Output 1

1 2 3

Sample Input 2

3 3

Sample Output 2

-1

Solution in Rust (1.15.1) (judge verdict: Accepted)

#![allow(unused_imports)]
#![allow(non_snake_case)]
use std::cmp::*;
use std::collections::*;
use std::io::Write;

#[allow(unused_macros)]
macro_rules! debug {
    ($($e:expr),*) => {
        #[cfg(debug_assertions)]
        $({
            let (e, mut err) = (stringify!($e), std::io::stderr());
            writeln!(err, "{} = {:?}", e, $e).unwrap()
        })*
    };
}

fn main() {
    let v = read_vec::<i64>();
    let (n, k) = (v[0], v[1]);
    let ab = (k..k + 2 * n).collect::<Vec<_>>();
    let c = (k + 2 * n..k + 3 * n).collect::<Vec<_>>();
    if c.iter().sum::<i64>() < ab.iter().sum::<i64>() {
        println!("-1");
        return;
    }
    let longer_oe_len = n - n / 2;
    let mut answers = vec![];
    for i in 0..longer_oe_len {
        answers.push((k + i, k + 2 * n - longer_oe_len + i, k + 2 * n + 2 * i));
    }
    let shorter_oe_len = n / 2;
    for i in 0..shorter_oe_len {
        answers.push((k + longer_oe_len + i, k + n + i, k + 2 * n + 2 * i + 1));
    }
    for ans in answers {
        println!("{} {} {}", ans.0, ans.1, ans.2);
    }
}

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()
}