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Consider a complete graph with $N$ vertices. Find $K$ spanning trees that are edge-disjoint.
The leftmost figure above shows a complete graph with four vertices. The two figures to the right are two edge-disjoint spanning trees of this graph.
You are given two integers $N$ and $K$ on a single line ($2 \le N \le 10^4$, $1 \le K \le 100$).
If there is no tuple of $K$ spanning trees that satisfies the conditions, print $-1$.
Otherwise, print $K$ spanning trees. Each spanning tree must be printed on $N - 1$ lines. The $i$-th line must contain two space-separated integers: the two endpoints of the $i$-th edge. The vertices are numbered $1$ through $N$. You may print an empty line between consecutive trees.
1 2 1 4 2 3 1 3 2 4 3 4