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 n, maxb, t, A[100005], f[100005], d[100005], cnt, pos, tree[100005];
void init() {
  memset(f, 0, sizeof(f));
  memset(d, 0, sizeof(d));
  memset(tree, 0, sizeof(tree));
  cnt = 0;
}
int lowbit(int x) { return x & -x; }
void updata(int x, int num) {
  while (x <= 100000) {
    tree[x] = max(tree[x], num);
    x += lowbit(x);
  }
}
int Ans(int x) {
  int ans = 0;
  while (x > 0) {
    ans = max(ans, tree[x]);
    x -= lowbit(x);
  }
  return ans;
}
int main() {
  int T;
  scanf("%d%d%d%d", &T, &n, &maxb, &t);
  while (T--) {
    for (int i = 1; i <= n; ++i) scanf("%d", &A[i]);
    if (t >= maxb) {
      sort(A + 1, A + n + 1);
      printf("%d\n", unique(A + 1, A + n + 1) - A - 1);
    } else {
      int ans = 0, cur;
      for (int i = 1; i <= t; ++i)
        for (int j = 1; j <= n; ++j) {
          cur = Ans(A[j] - 1) + 1;
          if (cur > d[j]) {
            d[j] = cur;
            ans = max(ans, d[j]);
            updata(A[j], d[j]);
          }
        }
      printf("%d\n", ans);
      init();
    }
  }
}
