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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, …, 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 ≤ N ≤ 5 and 1 ≤ G ≤ 20. The next G lines are of the format “Mi ai1 ai2 … aiN” where 1 ≤ Mi ≤ 20 and ai1, …, aiN is a permutation of the integers 1, …, N. Mi is the number of individuals in the ith group, and ai1, …, aiN 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.
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
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