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 RI() {
  int x;
  scanf("%d", &x);
  return x;
}
const int N = 100000;
int a[N], dp[N], b[N + 1];
int main() {
  int k = RI(), n = RI(), maxb = RI(), t = RI();
  while (k--) {
    for (int i = (0); i < (n); i++) a[i] = RI();
    if (t >= min(maxb, n)) {
      sort(a, a + n);
      printf("%d\n", int(unique(a, a + n) - a));
    } else {
      int maxdp = 0;
      fill_n(dp, n, 0);
      fill_n(b, n + 1, 0);
      for (int i = (0); i < (t); i++)
        for (int j = (0); j < (n); j++) {
          for (; dp[j] <= maxdp && b[dp[j]] < a[j]; dp[j]++)
            ;
          b[dp[j]] = a[j];
          maxdp = max(maxdp, dp[j]);
        }
      printf("%d\n", maxdp);
    }
  }
}
