Spanning Trees

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문제 설명

예제2

문제

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.

입력

You are given two integers $N$ and $K$ on a single line ( $2 \le N \le 10^4$ , $1 \le K \le 100$ ).

출력

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.