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;
const double eps = 1e-8;
int k, n, maxb, t;
int a[300000];
int b[300000];
int mi[300000];
int last[300000];
int main() {
  scanf("%d%d%d%d", &k, &n, &maxb, &t);
  for (int now = 1; now <= k; ++now) {
    int n = ::n;
    for (int i = 0; i < n; ++i) {
      scanf("%d", &a[i]);
      b[i] = a[i];
      last[i] = 0;
    }
    sort(b, b + n);
    int diff = unique(b, b + n) - b;
    for (int i = 0; i < n; ++i) {
      a[i] = lower_bound(b, b + diff, a[i]) - b;
    }
    int maxAnswer = diff;
    if (t >= maxAnswer) {
      printf("%d\n", maxAnswer);
      continue;
    }
    n = unique(a, a + n) - a;
    for (int i = 0; i <= maxAnswer; ++i) {
      mi[i] = 0x7fffffff;
    }
    mi[0] = 0;
    int ans = 0;
    for (int i = 0; i < t && i < maxAnswer; ++i) {
      int *ptr = a;
      for (int j = 0; j < n; ++j, ++ptr) {
        register int p = *ptr;
        int low = last[j], high = maxAnswer - 1;
        if (last[j] + 1 == p + 1) {
          low = high = last[j];
        }
        while (low < high) {
          int mid = 1 + ((low + high) >> 1);
          if (mi[mid] < p) {
            low = mid;
          } else {
            high = mid - 1;
          }
        }
        last[j] = low;
        if (low + 1 > ans) {
          ans = low + 1;
          if (ans == maxAnswer) {
            break;
          }
        }
        if (p < mi[low + 1]) {
          mi[low + 1] = p;
        }
      }
      if (ans == maxAnswer) {
        break;
      }
    }
    cout << ans << endl;
  }
}
