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 maxn = 3e5 + 10;
int n, T;
long long pre[maxn], dp[maxn], suf[400][200], res[400], bac[maxn], a[maxn];
int main() {
  cin >> n >> T;
  for (int i = 1; i <= n; i++) {
    cin >> a[i];
    bac[a[i]]++;
  }
  for (int i = 1; i < n && i < T; i++) {
    for (int j = 1; j <= n; j++) {
      a[i * n + j] = a[j];
    }
  }
  int len = min(n, T) * n;
  long long res = 0;
  for (int i = 1; i <= len; i++) {
    dp[i] = 1;
    for (int j = 1; j < i; j++) {
      if (a[i] >= a[j]) dp[i] = max(dp[i], dp[j] + 1);
    }
    res = max(res, dp[i]);
  }
  if (T <= n) {
    cout << res;
    return 0;
  }
  int mx = 0;
  for (int i = 1; i <= 300; i++) {
    mx = max(1LL * mx, bac[i]);
  }
  cout << res + (T - n) * mx << endl;
}
