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 arr[100], fre[301];
int lis(int len, int k) {
  int c, i, h, pos = 0;
  vector<int> A(len * k);
  for (c = 0; c < len * k; ++c) {
    h = arr[c % len];
    for (i = pos - 1; i >= 0; --i)
      if (A[i] <= h) break;
    if (i + 1 == pos) ++pos;
    A[i + 1] = h;
  }
  return pos;
}
int main() {
  int n, m, z = 0;
  cin >> n >> m;
  for (int i = 0; i <= 300; ++i) fre[i] = 0;
  for (int i = 0; i < n; ++i) {
    cin >> arr[i];
    z = max(z, ++fre[arr[i]]);
  }
  cout << lis(n, min(n, m)) + max(m - n, 0) * z << endl;
}
