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 k, n, t, maxB, cnt, ans;
int a[100010], bz[100010], f[100010];
void R(register int &x) {
  char c = getchar();
  x = 0;
  for (; !isdigit(c); c = getchar())
    ;
  for (; isdigit(c); x = (x << 3) + (x << 1) + c - '0', c = getchar())
    ;
}
int main() {
  R(k), R(n), R(maxB), R(t);
  for (register int i = 1; i <= k; i++) {
    memset(bz, 0, sizeof bz), cnt = 0;
    for (register int j = 1; j <= n; j++) {
      R(a[j]);
      if (!bz[a[j]]) cnt++;
      bz[a[j]] = 1;
    }
    if (t >= maxB)
      printf("%d\n", cnt);
    else {
      ans = 0, memset(f, 0, sizeof f);
      for (register int j = 1; j <= n * t; j++) {
        register int t = (j - 1) % n + 1, len = f[a[t]] + 1;
        for (register int k = a[t] + 1; k <= maxB; k++)
          if (f[k] >= len)
            break;
          else
            f[k] = len;
        ans = ((ans) > (len) ? (ans) : (len));
      }
      printf("%d\n", ans);
    }
  }
}
