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;
int n, t;
int a[110];
int cnt[310];
int mx;
int main() {
  ios_base::sync_with_stdio(0);
  cin >> n >> t;
  for (int i = 0; i < n; i++) {
    cin >> a[i];
    cnt[a[i]]++;
    mx = max(mx, cnt[a[i]]);
  }
  vector<int> v;
  for (int j = 0; j < min(t, n / 2); j++) {
    for (int i = 0; i < n; i++) {
      int idx = upper_bound(v.begin(), v.end(), a[i]) - v.begin();
      if (idx == v.size()) {
        v.push_back(a[i]);
      } else {
        v[idx] = a[i];
      }
    }
  }
  cout << v.size() + mx * (t - min(t, n / 2)) << "\n";
  return 0;
}
