You are given an array of positive integers a1, a2, ..., an × T of length n × T. We know that for any i > n it is true that ai = ai - n. Find the length of the longest non-decreasing sequence of the given array.

Input

The first line contains two space-separated integers: n, T (1 ≤ n ≤ 100, 1 ≤ T ≤ 107). The second line contains n space-separated integers a1, a2, ..., an (1 ≤ ai ≤ 300).

Output

Print a single number — the length of a sought sequence.

Examples

Input

4 3
3 1 4 2


Output

5

Note

The array given in the sample looks like that: 3, 1, 4, 2, 3, 1, 4, 2, 3, 1, 4, 2. The elements in bold form the largest non-decreasing subsequence. 
#include <bits/stdc++.h>
using namespace std;
const int N = 350;
int a[N], cnt[N], d[N] = {0}, n, T;
int main() {
  cin >> n >> T;
  for (int i = 1; i <= n; i++) scanf("%d", &a[i]), cnt[a[i]]++;
  int max_ = 0;
  for (int i = 1; i <= n; i++) max_ = max(max_, cnt[a[i]]);
  int min_ = min(T, 200);
  for (int i = 1; i <= min_; i++) {
    for (int j = 1; j <= n; j++) {
      int te = 0;
      for (int k = 1; k <= n; k++)
        if (a[k] <= a[j]) {
          te = max(te, d[k] + 1);
        }
      d[j] = te;
    }
  }
  int res = 0;
  for (int i = 1; i <= n; i++) res = max(res, d[i]);
  cout << res + (T - min_) * max_ << endl;
  return 0;
}
