Archery Competition Ranking

The Kingdom's annual archery competition has just concluded, and you, as the head statistician, must process the results. There are N participants, each assigned a unique ID from 1 to N. The competition is held over K rounds. In each round, every participant scores some points. Your task is to compute the total score for each participant and determine the top M participants.

The total score for participant i is given by the formula:

\(S_i = \sum_{j=1}^K s_{ij}\)

where \(s_{ij}\) is the score of participant i in round j. In case of ties, the participant with the smaller ID is ranked higher. Finally, output the IDs of the top M participants in descending order of their total scores.

inputFormat

The input is given via standard input (stdin) in the following format:

N K M
s11 s12 ... s1N
s21 s22 ... s2N
...
sK1 sK2 ... sKN

Here, the first line contains three space-separated integers: N (number of participants), K (number of rounds), and M (number of top participants to select). Each of the following K lines contains N integers representing the scores of the participants in that round.

outputFormat

Output via standard output (stdout) a single line containing the IDs of the top M participants, separated by a single space, in descending order of their total scores. In case of a tie, the participant with the smaller ID should come first.

5 3 3
10 20 30 40 50
25 15 5 45 10
5 10 20 35 40

4 5 3