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[10010], dp[310], num[10010];
int main() {
  int n, t, maxn = 0, result = 0;
  cin >> n >> t;
  int t1 = min(n, t);
  memset(num, 0, sizeof(num));
  memset(dp, 0, sizeof(dp));
  for (int i = 1; i <= n; i++) {
    cin >> a[i];
    num[a[i]]++;
    maxn = max(maxn, num[a[i]]);
  }
  int m = t1 * n;
  for (int i = 1; i <= m; i++) {
    if (i > n) a[i] = a[i - n];
  }
  for (int i = 1; i <= m; i++) {
    dp[a[i]]++;
    for (int j = a[i] - 1; j >= 0; j--) dp[a[i]] = max(dp[a[i]], dp[j] + 1);
    result = max(dp[a[i]], result);
  }
  result += maxn * (t - t1);
  cout << result << endl;
  return 0;
}
