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 main() {
  int n, t;
  cin >> n >> t;
  int niza[10105];
  for (int k = 0; k < n; k++) {
    cin >> niza[k];
    for (int i = k + n; i < 10105; i += n) {
      niza[i] = niza[k];
    }
  }
  int rez[201];
  int dp[10105];
  int pos[305];
  for (int j = 1; j <= 101; j++) {
    dp[0] = 1;
    rez[j] = 1;
    memset(pos, -1, sizeof(pos));
    pos[niza[0]] = 1;
    int lim = n * j;
    for (int k = 1; k < lim; k++) {
      dp[k] = 1;
      for (int i = niza[k]; i > 0; i--) {
        dp[k] = max(dp[k], pos[i] + 1);
      }
      pos[niza[k]] = max(pos[niza[k]], dp[k]);
      rez[j] = max(rez[j], dp[k]);
    }
  }
  if (t <= 101) {
    cout << rez[t] << endl;
  } else {
    int dif = rez[101] - rez[100];
    cout << rez[101] + dif * (t - 101) << endl;
  }
  return 0;
}
