문제 정보

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Given the voting preferences of a population of M people, you are to determine the winner of an election among N candidates, numbered 1, \cdots ,N. For this problem, the M people are partitioned into G “groups”where all members within a group have the same voting preferences. The candidate preferences for a group are specified by listing candidates from most preferred to least preferred. Election results are determined by an instant-runoff voting procedure.
In this method, the first choices of the M people in the population are counted and the least popular candidate is eliminated. In the event of a tie, the highest-numbered candidate is eliminated. Then, the eliminated candidate is removed from the preference list of all M individuals in the population, and again the least popular candidate is eliminated. This process repeats until only a single candidate is left.


The input test file will contain multiple test cases. Each input test case begins with a single line containing the integers G and N where 2 \le N \le 5 and 1 \le G \le 20. The next G lines are of the format “M_i\;a_{i_1}\;a_{i_2}\; \cdots a_{i_N}” where 1 \le Mi \le 20 and a_{i_1}, \cdots , a_{i_N} is a permutation of the integers 1, \cdots ,N. M_i is the number of individuals in the ith group, and a_{i_1}, \cdots , a_{i_N} is the ordering of the N candidates from most preferred to
least preferred for the ith group. The end-of-file is marked by a test case with G = N = 0 and should not be processed.


For each input case, the program should print the winner of the election on a single line.

예제 입력

3 4
10 1 4 2 3
15 3 2 1 4
12 4 3 2 1
3 2
10 1 2
10 1 2
20 2 1
0 0

예제 출력



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