Club presidency election is going on at the university. As the club members, you have decided for the following rules:

• Everybody can vote for two candidates.
• If one of the votes for a non existing candidate, only that part of the vote is invalid.
• If somebody votes twice for the same person, all the vote is invalid.
• If a candidate is in the first position, (s)he takes 2 points
• if a candidate is in the second position, (s)he gets 1 point.

Question: Write a program that is going to calculate the votes received and show the IDs of top m candidates.

Input specification
In the first line, you will be given three integers:

1. The number of people voting (n) where n is between 1 and 60,000
2. The number of candidates (k) where k is between 1 and 60,000
3. The number of top (m) candidates to show in the end where m is between 1 and 10,000

Output specification
Show IDs of top m candidates. If there are two candidates with the same points, first show the one whose ID is smaller.

Explanation: There are 4 candidates and 5 students voted.

1. The first student voted for candidate 5 (which is invalid) and the second candidate (1 points).
2. The second student gave two points to the third candidate and 1 point to the second candidate
3. The third student gave two points to the second candidate and 1 point to the fourth candidate
4. The fourth and fifth students voted for the same person twice, so, the votes are invalid.