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;
const int maxn = 10005;
int lis[maxn], num[maxn];
map<int, int> cnt;
int n, m;
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cin >> n >> m;
  int maxlen = 0;
  for (int i = 0; i < n; ++i) {
    cin >> num[i];
    ++cnt[num[i]];
    maxlen = max(maxlen, cnt[num[i]]);
  }
  int len = m > n ? n * n : n * m;
  for (int i = n; i < len; ++i) num[i] = num[i - n];
  int ans = 0;
  for (int i = 0; i < len; ++i) {
    int pos = upper_bound(lis, lis + ans, num[i]) - lis;
    if (pos == ans)
      lis[ans++] = num[i];
    else
      lis[pos] = num[i];
  }
  if (m > n) ans += (m - n) * maxlen;
  cout << ans << endl;
  return 0;
}
