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 = 100050;
int b[Maxn], vis[Maxn], v[Maxn];
long long f[Maxn];
int main() {
  int k, n, maxb, t;
  scanf("%d%d%d%d", &k, &n, &maxb, &t);
  while (k--) {
    long long ans = 0, tot = 0, tmp = 0;
    memset(vis, 0, sizeof vis);
    memset(v, 0, sizeof v);
    for (int i = 1; i <= n; ++i) {
      scanf("%d", &b[i]);
      if (!vis[b[i]]) tot++;
    }
    t = min(t, maxb);
    memset(f, 0, sizeof f);
    for (int i = 1, j = 1; j <= t;) {
      int x = b[i];
      if (f[x] == f[x - 1] + 1)
        tmp++, v[f[x]] = 1;
      else if (v[f[x]])
        tmp--, v[f[x]] = 0;
      f[x] = f[x - 1] + 1;
      for (int num = x + 1; num <= maxb; ++num)
        if (f[num] < f[x])
          f[num] = f[x];
        else
          break;
      ++i;
      if (i > n) i -= n, j++;
    }
    printf("%lld\n", f[maxb]);
  }
  return 0;
}
