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#663. 生成树

Estadísticas

考虑一个具有 $N$ 个顶点的完全图。请找出 $K$ 棵边不相交的生成树。

最左侧的图展示了一个具有四个顶点的完全图。右侧的两个图是该图的两棵边不相交的生成树。

输入格式

输入包含两个整数 $N$ 和 $K$,位于同一行中 ($2 \le N \le 10^4$, $1 \le K \le 100$)。

输出格式

如果不存在满足条件的 $K$ 棵生成树,输出 $-1$。

否则,输出 $K$ 棵生成树。每棵生成树必须占用 $N-1$ 行输出。第 $i$ 行必须包含两个用空格分隔的整数:第 $i$ 条边的两个端点。顶点编号为 $1$ 到 $N$。你可以在相邻的树之间打印一个空行。

样例

样例输入 1

4 2

样例输出 1

1 2
1 4
2 3
1 3
2 4
3 4

样例输入 2

4 3

样例输出 2

-1

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