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[110], b[300300], c[300300];
int main() {
  int n, T;
  while (cin >> n >> T) {
    map<int, int> mp;
    for (int i = 0; i < n; i++) cin >> a[i], mp[a[i]]++;
    int mx = -1;
    for (int i = 0; i < n; i++) mx = std::max(mx, mp[a[i]]);
    if (T <= 3000) {
      int tot = 0;
      for (int i = 1; i <= T; i++) {
        for (int j = 0; j < n; j++) b[tot++] = a[j];
      }
      int ss = 1;
      c[0] = b[0];
      for (int i = 1; i < tot; i++) {
        int tt = upper_bound(c, c + ss, b[i]) - c;
        if (tt == ss) ss++;
        c[tt] = b[i];
      }
      cout << ss << endl;
      continue;
    }
    int tot = 0;
    int ans = mx * (T - 3000);
    T -= 3000;
    for (int i = 1; i <= 3000; i++) {
      for (int j = 0; j < n; j++) b[tot++] = a[j];
    }
    int ss = 1;
    c[0] = b[0];
    for (int i = 1; i < tot; i++) {
      int tt = upper_bound(c, c + ss, b[i]) - c;
      if (tt == ss) ss++;
      c[tt] = b[i];
    }
    ans += ss;
    cout << ans << endl;
  }
  return 0;
}
