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 a[100010], f[100010], t, maxb;
int LIS(const int &n) {
  int i, size = 1, ss;
  int l, r, z;
  f[0] = 0;
  for (int ti = 0; ti < t; ++ti) {
    ss = size;
    for (i = 0; i < n; ++i) {
      if (a[i] <= f[ti]) continue;
      l = ti;
      r = size;
      while (l + 1 < r) {
        z = (l + r) >> 1;
        if (f[z] < a[i])
          l = z;
        else
          r = z;
      }
      f[l + 1] = a[i];
      if (l == size - 1) size++;
    }
    if (size == ss) return size;
  }
  return size;
}
int main(void) {
  int i, n, T;
  scanf("%d", &T);
  scanf("%d%d%d", &n, &maxb, &t);
  t = min(maxb, t);
  while (T--) {
    for (i = 0; i < n; ++i) scanf("%d", &a[i]);
    printf("%d\n", LIS(n) - 1);
  }
  return 0;
}
