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[101];
int cnt[301];
int dp[30001];
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cin >> n >> T;
  int parsacnt = 0;
  for (int i = 0; i < n; i++) {
    cin >> a[i];
    cnt[a[i]]++;
    if (cnt[a[i]] > parsacnt) parsacnt = cnt[a[i]];
  }
  int lim = min(T, 300);
  int res = 0;
  for (int i = 0; i < lim * n; i++) {
    dp[i] = 1;
    for (int j = max(i - n, 0); j < i; j++) {
      if (a[j % n] <= a[i % n]) dp[i] = max(dp[i], dp[j] + 1);
    }
    if (dp[i] > res) res = dp[i];
  }
  res += (T - lim) * parsacnt;
  cout << res << "\n";
}
