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:

$a_1$ $b_1$ $c_1$

$:$

$a_N$ $b_N$ $c_N$

1 1

1 2 3

3 3

-1