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 int MAXN = 110000;
int n, t;
int b[MAXN];
pair<int, int> _b[MAXN];
int ans[MAXN];
int ptr[MAXN];
void solve() {
  for (int i = 0; i < n; i++) {
    scanf("%d", &_b[i].first);
    _b[i].second = i;
  }
  sort(_b, _b + n);
  int maxc = 0;
  for (int i = 0; i < n; i++) {
    if (i && _b[i].first != _b[i - 1].first) maxc++;
    b[_b[i].second] = maxc;
  }
  maxc++;
  memset(ans, 0x3f, sizeof(ans));
  memset(ptr, 0, sizeof(ptr));
  int tmp;
  for (int i = 0; i < t && i < maxc; i++) {
    for (int j = 0; j < n; j++) {
      tmp = b[j];
      while (ans[ptr[tmp]] < tmp) ptr[tmp]++;
      ans[ptr[tmp]] = tmp;
    }
  }
  cout << *max_element(ptr, ptr + maxc) + 1 << endl;
}
int main() {
  int tests;
  scanf("%d %d %*d %d", &tests, &n, &t);
  for (int i = 0; i < tests; i++) solve();
  return 0;
}
