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 dp[1000000], arr[1000000], arr2[300], n, t, maxn = 1, mx = 1;
int main() {
  cin >> n;
  cin >> t;
  for (int i = 0; i < n; ++i) {
    cin >> arr[i];
    arr2[arr[i]]++;
    mx = max(mx, arr2[arr[i]]);
    dp[i] = 1;
  }
  int k = min(n, t);
  for (int i = n; i < n * k; ++i) {
    arr[i] = arr[i - n];
    dp[i] = 1;
  }
  for (int i = 0; i < n * k; ++i) {
    for (int j = 0; j < i; j++) {
      if (arr[i] >= arr[j]) {
        dp[i] = max(dp[i], dp[j] + 1);
        maxn = max(maxn, dp[i]);
      }
    }
  }
  if (t > n) {
    maxn += mx * (t - n);
  }
  cout << maxn << endl;
  return 0;
}
