Restore the Tree

题意翻译

Petya 有一个由 $n$ 个点构成的树。 但 Petya 只记得这颗树的 $k$ 个关键点与所有点 $n$ 的距离. 你的任务是构造一种树的方案使其满足 Petya 记忆中的树，若无法构成则输出 $-1$。 $2 \le n \le 30000,1 \le k \le \min(200, n)$

题目描述

Petya had a tree consisting of $ n $ vertices numbered with integers from $ 1 $ to $ n $ . Accidentally he lost his tree. Petya remembers information about $ k $ vertices: distances from each of them to each of the $ n $ tree vertices. Your task is to restore any tree that satisfies the information that Petya remembers or report that such tree doesn't exist.

输入输出格式

输入格式

The first line contains two integers $ n $ and $ k $ ( $ 2<=n<=30000 $ , $ 1<=k<=min(200,n) $ ) — the number of vertices in the tree and the number of vertices about which Petya remembers distance information. The following $ k $ lines contain remembered information. The $ i $ -th line contains $ n $ integers $ d_{i,1},d_{i,2},...,d_{i,n} $ ( $ 0<=d_{i,j}<=n-1 $ ), where $ d_{i,j} $ — the distance to $ j $ -th vertex from the $ i $ -th vertex that Petya remembers.

输出格式

If there are no suitable trees, print -1. In the other case, print $ n-1 $ lines: each line should contain two vertices connected by edge in the required tree. You can print edges and vertices in an edge in any order. The tree vertices are enumerated from $ 1 $ to $ n $ . If there are many solutions print any of them.

输入输出样例

输入样例 #1

5 2
0 1 2 3 2
2 1 0 1 2

输出样例 #1

2 1
3 2
4 3
5 2

输入样例 #2

3 1
1 2 1

输出样例 #2

-1

说明

Picture for the first sample: