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;
const int E = 1e5 + 9;
int dp[E];
int a[E];
int c[E];
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  int n, t;
  cin >> n >> t;
  int M = 0;
  for (int i = 0; i < n; i++) {
    int x;
    cin >> x;
    c[x]++;
    M = max(M, c[x]);
    for (int j = 0; j < n; j++) {
      a[j * n + i] = x;
    }
  }
  fill(dp, dp + E, 500);
  int m = min(n, t);
  for (int i = 0; i < n * m; i++) {
    dp[upper_bound(dp, dp + E, a[i]) - dp] = a[i];
  }
  int k = lower_bound(dp, dp + E, 400) - dp;
  if (t > n) {
    k += (t - n) * M;
  }
  cout << k;
  return 0;
}
