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 MAX_N = 1e4 + 5;
long long s[MAX_N], cnt[301];
int main() {
  vector<int> ans;
  int n, T;
  cin >> n >> T;
  for (int i = 0; i < n; i++) {
    cin >> s[i];
    cnt[s[i]]++;
  }
  long long mx = 0;
  for (int i = 1; i <= 300; i++) mx = max(mx, cnt[i]);
  for (int i = 0; i < min(n, T); i++) {
    for (int j = 0; j < n; j++) {
      int ind = upper_bound(ans.begin(), ans.end(), s[j]) - ans.begin();
      if (ind < ans.size())
        ans[ind] = s[j];
      else
        ans.push_back(s[j]);
    }
  }
  long long num = ans.size();
  if (T >= n) num += mx * (T - n);
  cout << num << endl;
  return 0;
}
