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; 
  * <image> (1 ≤ i ≤ n × t), where operation <image> 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

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

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

3 3 5 2
3 2 1
1 2 3
2 3 1


Output

2
3
3
#include <bits/stdc++.h>
using namespace std;
int n, m, k, t, b[100100];
int d[100100];
void read(void) {
  scanf("%d%d%d%d", &k, &n, &m, &t);
  t = min(t, n);
  t = min(t, m);
}
void kill(void) {
  for (int i = 0; i < n; ++i) scanf("%d", b + i);
  for (int j = 0; j <= m; ++j) d[j] = 0;
  for (int i = 0; i < t; ++i)
    for (int j = 0; j < n; ++j)
      if (1 + d[b[j] - 1] > d[b[j]]) {
        int x = b[j], k = x + 1;
        d[x] = d[x - 1] + 1;
        while (k <= m && d[k] < d[x]) d[k++] = d[x];
      }
  int ans = 0;
  for (int j = 0; j <= m; ++j) ans = max(ans, d[j]);
  printf("%d\n", ans);
}
int main() {
  read();
  for (int i = 0; i < k; ++i) kill();
  return 0;
}
