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 a[100010], c[100010];
int k, n, maxb, t;
int get_unique();
int calc();
int main() {
  scanf("%d%d%d%d", &k, &n, &maxb, &t);
  while (k--) {
    for (int i = 1; i <= n; i++) scanf("%d", a + i);
    if (t >= maxb) {
      printf("%d\n", get_unique());
    } else {
      printf("%d\n", calc());
    }
  }
}
int get_unique() {
  sort(a + 1, a + n + 1);
  int count = 1;
  for (int i = 2; i <= n; i++)
    if (a[i] != a[i - 1]) ++count;
  return count;
}
int getmax(int cur) {
  int ans = 0;
  while (cur) {
    ans = max(ans, c[cur]);
    cur -= (cur & (-cur));
  }
  return ans;
}
void update(int cur, int val) {
  while (cur <= maxb) {
    c[cur] = max(c[cur], val);
    cur += (cur & (-cur));
  }
}
int calc() {
  static int ans[100010];
  memset(ans, 0, sizeof ans);
  memset(c, 0, sizeof c);
  for (int i = 1; i <= t; i++)
    for (int j = 1; j <= n; j++) {
      int now = getmax(a[j] - 1) + 1;
      if (now > ans[j]) {
        ans[j] = now;
        update(a[j], now);
      }
    }
  int maxn = 0;
  for (int i = 1; i <= n; i++) maxn = max(ans[i], maxn);
  return maxn;
}
