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[310], c[310];
int n, t, k, res = 0, M = 0;
int main() {
  cin >> n >> t;
  for (int i = 0; i < n; ++i) {
    cin >> a[i];
    M = max(M, ++b[a[i]]);
  }
  for (int i = 0; i < min(n * 2, t) * n; ++i) {
    k = 1;
    for (int j = 1; j <= a[i % n]; ++j) k = max(k, c[j] + 1);
    c[a[i % n]] = k;
    res = max(res, k);
  }
  cout << res + max((t - n * 2) * M, 0);
}
