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, MAX_B, T, B[200010];
bool used[200010];
void solve() {
  int M = 0;
  memset(used, 0, sizeof(used));
  for (int i = 0; i < N; i++) {
    scanf("%d", B + i);
    M += !used[B[i]];
    used[B[i]] = true;
  }
  if (M <= T) {
    printf("%d\n", M);
    return;
  }
  int dp[200010] = {};
  for (int i = 0; i < T; i++) {
    for (int j = 0; j < N; j++) {
      for (int k = B[j] + 1; k <= MAX_B + 1; k++) {
        if (dp[k] > dp[B[j]]) break;
        dp[k] = dp[B[j]] + 1;
      }
    }
  }
  int ans = 0;
  for (int i = 0; i <= MAX_B + 1; i++) {
    ans = max(ans, dp[i]);
  }
  printf("%d\n", ans);
}
int main() {
  int K;
  scanf("%d%d%d%d", &K, &N, &MAX_B, &T);
  while (K--) solve();
  return 0;
}
