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[10050];
int num[10050];
int a[10050];
int main() {
  int n, t, mnum = 0;
  cin >> n >> t;
  memset(num, 0, sizeof num);
  for (int i = 0; i < n; i++) {
    cin >> a[i];
    num[a[i]]++;
    mnum = max(mnum, num[a[i]]);
  }
  int mm = min(n, t);
  int T = mm, cnt = 0;
  while (T--) {
    cnt += n;
    for (int i = 0; i < n; i++) a[i + cnt] = a[i];
  }
  int ans = 0;
  int len = 1;
  for (int i = 0; i < mm * n; i++) {
    dp[i]++;
    for (int j = 0; j < i; j++) {
      if (a[i] >= a[j]) dp[i] = max(dp[i], dp[j] + 1);
    }
    len = max(len, dp[i]);
  }
  ans = len + (t - mm) * mnum;
  printf("%d\n", ans);
  return 0;
}
