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 a[1000005], cnt[305], f[1000005];
int main() {
  int n, t, ans = 1;
  cin >> n >> t;
  int maxl = n * min(n, t);
  for (int i = 1; i <= n; i++) cin >> a[i], cnt[a[i]]++;
  for (int i = n + 1; i <= maxl; i++) a[i] = a[i - n];
  f[1] = 1;
  for (int i = 2; i <= maxl; i++) {
    for (int j = 1; j < i; j++) {
      if (a[j] <= a[i]) f[i] = max(f[i], f[j]);
    }
    ans = max(ans, ++f[i]);
  }
  int aans = 0;
  for (int i = 1; i <= 300; i++) aans = max(aans, cnt[i]);
  cout << ans + (max(t, n) - n) * aans << endl;
  return 0;
}
