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;
map<int, int> mp;
int num[10050], dp[10050];
int main() {
  int n, m;
  scanf("%d%d", &n, &m);
  for (int i = 0; i < n; i++) {
    scanf("%d", &num[i]);
    mp[num[i]]++;
  }
  int maxn = 0;
  for (int i = 0; i < n; i++) {
    maxn = max(maxn, mp[num[i]]);
  }
  for (int i = 0; i < 10050; i++) dp[i] = 99999999;
  int pos = n;
  if (m <= n) {
    for (int j = 1; j < m; j++) {
      for (int k = 0; k < n; k++) {
        num[pos++] = num[k];
      }
    }
    for (int i = 0; i < pos; i++) *upper_bound(dp, dp + pos, num[i]) = num[i];
    cout << lower_bound(dp, dp + pos, 99999999) - dp << endl;
  } else {
    for (int j = 1; j < n; j++) {
      for (int k = 0; k < n; k++) {
        num[pos++] = num[k];
      }
    }
    for (int i = 0; i < pos; i++) *upper_bound(dp, dp + pos, num[i]) = num[i];
    cout << lower_bound(dp, dp + pos, 99999999) - dp + (m - n) * maxn << endl;
  }
  return 0;
}
