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[105 * 105];
int scmax[105 * 105];
int fr[3 * 105], maxx, lim, sol;
int main() {
  cin >> n >> t;
  for (int i = 1; i <= n; ++i) {
    cin >> a[i];
    ++fr[a[i]];
    maxx = max(maxx, fr[a[i]]);
  }
  lim = n;
  for (int rep = 2; rep <= min(n, t); ++rep) {
    int i = n + 1;
    for (; i <= rep * n; ++i) a[i] = a[i - n];
    lim = i;
  }
  for (int i = 1; i <= lim; ++i)
    for (int j = 0; j < i; ++j)
      if (a[i] >= a[j]) {
        scmax[i] = max(scmax[i], scmax[j] + 1);
        sol = max(sol, scmax[i]);
      }
  t -= n;
  if (t > 0) sol += t * maxx;
  cout << sol;
  return 0;
}
