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 n, m, ns, t, arr[20010], cnt[305];
int solve(int mn, int mx) {
  vector<int> a(n + 1, 500);
  for (int i = 0; i < n; ++i) {
    if (arr[i] < mn || arr[i] > mx) continue;
    *upper_bound(a.begin(), a.end(), arr[i]) = arr[i];
  }
  for (int i = 0; i <= n; ++i)
    if (a[i] == 500) return i;
}
int main() {
  scanf("%d", &ns), scanf("%d", &t);
  n = ns * ns;
  for (int i = 0; i < ns; ++i) {
    scanf("%d", &arr[i]);
    if (++cnt[arr[i]] > cnt[arr[m]]) m = i;
  }
  for (int i = ns; i < 2 * n; ++i) arr[i] = arr[i - ns];
  if (t <= 2 * ns) {
    n = ns * t;
    cout << solve(0, 305);
    return 0;
  }
  cout << (t - 2 * ns) * cnt[arr[m]] + solve(0, arr[m]) + solve(arr[m], 305);
}
