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, ar[11000], dp[11000], as[350];
int main() {
  cin >> N >> T;
  for (int i = 1; i <= N; i++) scanf(" %d", &ar[i]), as[ar[i]]++;
  for (int i = N + 1; i <= N * N; i++) ar[i] = ar[i - N];
  int M = min(N * N, N * T);
  int res = 0;
  for (int i = 1; i <= M; i++) {
    int mx = 0;
    for (int j = i - 1; j; j--)
      if (ar[j] <= ar[i] && dp[j] > mx) mx = dp[j];
    dp[i] = mx + 1;
    res = max(res, mx + 1);
  }
  if (N >= T) {
    cout << res << endl;
    return 0;
  }
  T -= N;
  int qq = 0;
  for (int i = N * N - N + 1; i <= N * N; i++) {
    int t = res - dp[i];
    qq = max(qq, as[ar[i]] * T + dp[i] + t);
  }
  cout << qq << endl;
  return 0;
}
