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 g[10005], a[10005];
int n, t, ans, vis[305], maxv;
int main() {
  scanf("%d%d", &n, &t);
  for (int i = 1; i <= n; i++) {
    scanf("%d", &a[i]);
    vis[a[i]]++;
    maxv = max(maxv, vis[a[i]]);
  }
  int m = n, ts = min(n, t);
  for (int i = 1; i < ts; i++)
    for (int j = 1; j <= n; j++) a[++m] = a[j];
  for (int i = 0; i <= m; i++) g[i] = 0x7f7f7f7f;
  for (int i = 1; i <= m; i++) {
    int k = upper_bound(g + 1, g + m + 1, a[i]) - g;
    g[k] = a[i];
    ans = max(ans, k);
  }
  printf("%d\n", ans + maxv * max(0, t - ts));
  return 0;
}
