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 now[10005], dp[30005], aim[10005];
int main() {
  long long t;
  int n, maxn = 0;
  scanf("%d%lld", &n, &t);
  for (int i = 0; i < n; i++) {
    scanf("%d", &now[i]);
    aim[now[i]]++;
    maxn = max(aim[now[i]], maxn);
  }
  int l = n;
  while ((--t) && l < 10000) {
    for (int i = 0; i < n; i++) now[l++] = now[i];
  }
  int ans = 0;
  for (int i = 0; i < l; i++) {
    dp[i]++;
    for (int j = 0; j < i; j++)
      if (now[i] >= now[j]) dp[i] = max(dp[i], dp[j] + 1);
    ans = max(ans, dp[i]);
  }
  printf("%d\n", ans + t * maxn);
  return 0;
}
