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 n, t, l, ans, mx;
int a[10001], f[10001], b[301];
int main() {
  scanf("%d%d", &n, &t);
  l = n * min(n, t);
  for (int i = 1; i <= n; b[a[i]]++, mx = max(mx, b[a[i]]), i++)
    scanf("%d", &a[i]);
  for (int i = n + 1; i <= l; i++) a[i] = a[i - n];
  memset(f, 0x3f, sizeof(f));
  for (int i = 1; i <= l; i++) *upper_bound(f + 1, f + l + 1, a[i]) = a[i];
  ans = lower_bound(f + 1, f + l + 1, 0x3f3f3f3f) - f - 1;
  if (t > n) ans += (t - n) * mx;
  printf("%d\n", ans);
  return 0;
}
