When Can We Meet? — 2003年 会津大会 国内予選 問題A


[ Problem ]
 The ICPC committee would like to have its meeting as soon as possible to address every little issue of the next contest. However, members of the committee are so busy maniacally developing (possibly useless) programs that it is very difficult to arrange their schedules for the meeting. So, in order to settle the meeting date, the chairperson requested every member to send back a list of convenient dates by E-mail. Your mission is to help the chairperson, who is now dedicated to other issues of the contest, by writing a program that chooses the best date from the submitted lists. Your program should find the date convenient for the most members. If there is more than one such day, the earliest is the best.
 「委員会会議を開きたいので、 日程の調整をして欲しい。つまり、できるだけ多くの委員が出席できる日にちを決めること。出席できる委員の数が同数の日にちがいくつもある場合は、最も早い日にちにすること。」

[ Input ]
 The input has multiple data sets, each starting with a line containing the number of committee members and the quorum of the meeting.

   N Q
 Here, N, meaning the size of the committee, and Q meaning the quorum, are positive integers. N is less than 50, and, of course, Q is less than or equal to N.
 「N (50以下の正の整数)、委員の数。 Q (N以下の正の整数)、定足数(会議の成立に必要な最低出席者数)。」

 N lines follow, each describing convenient dates for a committee member in the following format.
   M Date1 Date2 … DateM
Here, M means the number of convenient dates for the member, which is an integer greater than or equal to zero. The remaining items in the line are his/her dates of convenience, which are positive integers less than 100, that is, 1 means tomorrow, 2 means the day after tomorrow, and so on. They are in ascending order without any repetition and separated by a space character. Lines have neither leading nor trailing spaces.
 「M (0以上の整数)、各委員の出席できる日にちリストの長さ。日にちリスト Datei (100以内の正の整数、1は明日、2は明後日を表す。)。」

 A line containing two zeros indicates the end of the input.

[ Output ]
 For each data set, print a single line containing the date number convenient for the largest number of committee members. If there is more than one such date, print the earliest. However, if no dates are convenient for more than or equal to the quorum number of members, print 0 instead.

[ Sample Input ]
3 2
2 1 4
3 3 4 8
3 2
4 1 5 8 9
3 2 5 9
5 2 4 5 7 9
3 3
2 1 4
3 2 5 9
2 2 4
3 3
2 1 2
3 1 2 9
2 2 4
0 0

[ Output for the Sample Input ]

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