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 num[100001], g[100011], cnt[301];
int main() {
  int n, T, t, ans, i, j, maxc;
  cin >> n >> T;
  maxc = 0;
  for (i = 1; i <= n; i++) {
    cin >> num[i];
    num[n + i] = num[i];
    cnt[num[i]]++;
    maxc = max(maxc, cnt[num[i]]);
  }
  t = min(T, 1000);
  for (i = 1; i <= t; i++) {
    for (j = 1; j <= n; j++) {
      num[(i - 1) * n + j] = num[j];
    }
  }
  memset(g, 0x3f, sizeof(g));
  ans = 0;
  for (i = 1; i <= n * t; i++) {
    int k = upper_bound(g + 1, g + n * t + 1, num[i]) - g;
    g[k] = num[i];
    ans = max(ans, k);
  }
  if (T > 1000) {
    ans += maxc * (T - 1000);
  }
  cout << ans << endl;
  return 0;
}
