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 x[10005];
int w[10005];
map<int, int> r;
int main() {
  int n, m;
  cin >> n >> m;
  int cnt = 0, maxx = 0;
  for (int i = 1; i <= n; ++i) {
    cin >> x[i];
    r[x[i]]++;
    maxx = max(maxx, r[x[i]]);
  }
  for (int i = n + 1; i <= n * min(n, m); ++i) x[i] = x[i - n];
  for (int i = 1; i <= n * min(n, m); ++i) {
    if (x[i] >= w[cnt]) {
      w[++cnt] = x[i];
    } else {
      int p = upper_bound(w + 1, w + cnt + 1, x[i]) - w;
      w[p] = x[i];
    }
  }
  if (m <= n)
    cout << cnt << endl;
  else
    cout << cnt + (m - n) * maxx << endl;
}
