Vera and Dogs

Vera has $N$ doghouses numbered $1$ to $N$ and $M$ dogs numbered $1$ to $M$, where $M = X \times N$. Doghouse $i$ must be the primary home of exactly $X$ dogs $P_{i,1}, \dots, P_{i,X}$ and the secondary home of exactly $X$ dogs $S_{i,1}, \dots, S_{i,X}$. Every dog has one primary home and one secondary home, and the two are different doghouses.

Every night at most one doghouse is closed for cleaning. A dog sleeps in its primary home when that home is open, and in its secondary home otherwise. On every possible night, including the night when no doghouse is closed, each open doghouse must hold at most $X + 1$ sleeping dogs.

Find an assignment that meets all of these conditions, or report that none exists.

The first line contains two integers $N$ and $X$ ($1 \le N, X \le 2017$, $X \times N \le 50000$).

If no valid assignment exists, print -1 on a single line.

Otherwise print $N$ lines. Line $i$ contains $2X$ integers: first the $X$ dogs whose primary home is doghouse $i$, in increasing order of dog number, then the $X$ dogs whose secondary home is doghouse $i$, in increasing order of dog number.

Several assignments can satisfy the conditions, so only this one counts as correct. For every $i$ from $1$ to $N$ and every $k$ from $1$ to $X$, the dog numbered $(i - 1)X + k$ has doghouse $i$ as its primary home and doghouse $((i + k - 1) \bmod N) + 1$ as its secondary home.

Doghouse numbers and dog numbers both start at $1$. The night on which no doghouse is closed also has to satisfy the capacity rule, and on that night each doghouse holds exactly the $X$ dogs that call it their primary home.