Milk Patterns

Farmer Ran has noticed that the quality of milk given by his cows
varies from day to day. On further investigation, he discovered
that although he can't predict the quality of milk from one day to
the next, there are some regular patterns in the daily milk quality.

To perform a rigorous study, he has invented a complex classification
scheme by which each milk sample is recorded as an integer between
0 and 1,000,000 inclusive. Furthermore, he has recorded data from
a single cow over N (1 <= N <= 20,000) days. He wishes to find the
longest pattern of samples which repeats identically at least K (2
<= K <= N) times.  This may include overlapping patterns -- 1 2 3
2 3 2 3 1 repeats 2 3 2 3 twice, for example.

Help Farmer Ran by finding the longest repeating subsequence in
the sequence of samples. It is guaranteed that at least one subsequence
is repeated at least K times.

PROBLEM NAME: patterns

INPUT FORMAT:

* Line 1: Two space-separated integers: N and K

* Lines 2..N+1: Line i+1 contains a single integer that is the quality
        of milk on day i

SAMPLE INPUT:

8 2
1
2
3
2
3
2
3
1

OUTPUT FORMAT:

* Line 1: One integer, the length of the longest pattern which occurs
        at least K times

SAMPLE OUTPUT:

4