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 main() {
  int n, t, a[110], dp[10010], len = 0, num[110], Max = 0;
  memset(num, 0, sizeof(num));
  scanf("%d%d", &n, &t);
  for (int i = 0; i < n; i++) {
    scanf("%d", &a[i]);
    num[a[i]]++;
    Max = max(Max, num[a[i]]);
  }
  int k = min(n, t);
  dp[len++] = a[0];
  for (int i = 1; i < n * k; i++) {
    if (a[i % n] >= dp[len - 1])
      dp[len++] = a[i % n];
    else
      dp[upper_bound(dp, dp + len, a[i % n]) - dp] = a[i % n];
  }
  if (t > n) {
    len += Max * (t - n);
  }
  printf("%d\n", len);
  return 0;
}
