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 len, n, m, i, j, id[100010], xlh, cnt[100010], f[100010], a[100010], ans;
int main() {
  scanf("%d%d", &n, &m);
  for (i = 1; i <= n; i++) {
    scanf("%d", &a[i]);
    id[i] = 1;
    cnt[a[i]]++;
  }
  len = min(n * n, n * m);
  for (i = n + 1; i <= len; i++) a[i] = a[i - n], id[i] = id[i - n] + 1;
  for (i = 1; i <= len; i++) id[i] = min(n, m) - id[i] + 1;
  for (i = len; i; i--) {
    f[i] = 1;
    for (j = i + 1; j <= len; j++)
      if (a[j] >= a[i]) f[i] = max(f[i], f[j] + 1);
    ans = max(ans, f[i]);
  }
  xlh = 0;
  if (m <= n) return printf("%d", ans), 0;
  for (i = 1; i <= 300; i++) xlh = max(xlh, cnt[i]);
  printf("%d", ans + xlh * (m - n));
}
