8980: The Game of Eating

Today, Fallleaves01 and his $n-1$ friends went out for dinner. They intend to order a total of $k$ dishes. To ensure everyone gets their favorite dish, they decided to take turns ordering one dish each in sequential order(i.e., 1st person, 2nd person, ..., $n$-th person, 1st person, ...) and repeat until they have ordered a total of $k$ dishes.

Please be aware that the dishes ordered by one person can be shared and tasted by everyone. To ensure a wide variety of flavors and experiences, it is important for individuals to avoid ordering the same dish multiple times.

There are a total of $m$ dishes available for selection. Everyone knows each person's preferences for every dish. This information is represented by an $n\times m$ matrix called $A$, where Ai,jA_{i,j}Ai,j denotes the degree to which the $i$-th person likes the $j$-th dish.

Assume that each person only cares about their own enjoyment of the dishes without considering others. In other words,if they ultimately choose dishes p1,p2...,pkp_1,p_2..., p_kp1,p2...,pk, person $i$ aims to maximize ∑1≤j≤kAi,pj\sum_{1 \leq j \leq k} A_{i,p_j}∑1≤j≤kAi,pj.

We also found that for every different 1≤x,y≤m,Ai,x≠Ai,y1 \leq x,y \leq m, A_{i,x} \neq A_{i,y}1≤x,y≤m,Ai,x=Ai,y.

Fallleaves01 is curious to know what dishes will be on the table if everyone makes optimal decisions.

The input consists of multiple test cases. The first line of each test case contains an integer $t$, indicating the number of test cases. The following lines describe each test case.
For each test case, the first line contains three integers $n$, $m$, and $k$ (1≤n≤2000,1≤k≤m≤20001 \leq n \leq 2000, 1 \leq k \le m \leq 20001≤n≤2000,1≤k≤m≤2000). These represent the number of people, the number of dishes, and the number of dishes planned to be ordered, respectively.
The next $n$ lines contain $m$ integers per line. The $j$-th number on the $i$-th line represents the degree to which the $i$-th person likes the $j$-th dish, denoted as Ai,jA_{i,j}Ai,j (1≤Ai,j≤1091 \leq A_{i,j} \leq 10^91≤Ai,j≤109).
It is guaranteed that the sum of $n$ and the sum of $m$ do not exceed $2000$.

For each test case, output a row of $k$ integers in increasing order, representing the final selected dishes.