Description:
Maxim loves sequences, especially those that strictly increase. He is wondering, what is the length of the longest increasing subsequence of the given sequence a?
Sequence a is given as follows:
- the length of the sequence equals n × t;
- $$a_i = b_{((i-1) \mod n)+1}$$ (1 ≤ i ≤ n × t), where operation $$( x \mod y )$$ means taking the remainder after dividing number x by number y.
Sequence s1, s2, ..., sr of length r is a subsequence of sequence a1, a2, ..., an, if there is such increasing sequence of indexes i1, i2, ..., ir (1 ≤ i1 < i2 < ... < ir ≤ n), that aij = sj. In other words, the subsequence can be obtained from the sequence by crossing out some elements.
Sequence s1, s2, ..., sr is increasing, if the following inequality holds: s1 < s2 < ... < sr.
Maxim have k variants of the sequence a. Help Maxim to determine for each sequence the length of the longest increasing subsequence.
Input Format:
The first line contains four integers k, n, maxb and t (1 ≤ k ≤ 10; 1 ≤ n, maxb ≤ 105; 1 ≤ t ≤ 109; n × maxb ≤ 2·107). Each of the next k lines contain n integers b1, b2, ..., bn (1 ≤ bi ≤ maxb).
Note that for each variant of the sequence a the values n, maxb and t coincide, the only arrays bs differ.
The numbers in the lines are separated by single spaces.
Output Format:
Print k integers — the answers for the variants of the sequence a. Print the answers in the order the variants follow in the input.
Note:
None