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 = 20000010;
int k, n, m, t;
int b[maxn];
int dp[maxn];
int gao[maxn];
int main() {
  while (~scanf("%d %d %d %d", &k, &n, &m, &t)) {
    t = min(t, min(n, m));
    while (k--) {
      for (int i = 1; i <= n; i++) scanf("%d", &b[i]);
      for (int i = 1; i <= n + 10; i++) gao[i] = maxn;
      gao[0] = 0;
      int cnt = 0;
      int ans = 0;
      for (int j = 1; j <= t; j++)
        for (int i = 1; i <= n; i++) {
          cnt++;
          if (j > 1)
            dp[cnt] = dp[cnt - n] - 1;
          else
            dp[cnt] = 0;
          while (gao[dp[cnt] + 1] < b[i]) dp[cnt]++;
          dp[cnt]++;
          if (gao[dp[cnt]] > b[i]) gao[dp[cnt]] = b[i];
          ans = max(ans, dp[cnt]);
        }
      printf("%d\n", ans);
    }
  }
}
