P6252 - Maxim and Increasing Subsequence

内存限制：256 MB 时间限制：2 S 标准输入输出

题目类型：传统评测方式：文本比较上传者：

提交：0 通过：0

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;
$\text{[math]}$ (1≤i≤n×t), where operation $\text{[math]}$ means taking the remainder after dividing number x by number y.

Sequence s₁,s₂,...,s_r of length r is a subsequence of sequence a₁,a₂,...,a_n, if there is such increasing sequence of indexes i₁,i₂,...,i_r (1≤i₁<i₂<... <i_r≤n), that a_{i_j}=s_j. In other words, the subsequence can be obtained from the sequence by crossing out some elements.

Sequence s₁,s₂,...,s_r is increasing, if the following inequality holds: s₁<s₂<...<s_r.

Maxim have k variants of the sequence a. Help Maxim to determine for each sequence the length of the longest increasing subsequence.

Input

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,...,b_n (1≤b_i≤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

Print k integers − the answers for the variants of the sequence a. Print the answers in the order the variants follow in the input.

Examples

Input

Output

2
3
3

6252: Maxim and Increasing Subsequence

题目描述