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;
const int maxn = 1e4 + 10;
int a[maxn];
int p[maxn];
int num[maxn];
int main() {
  int n, t;
  while (~scanf("%d%d", &n, &t)) {
    memset(num, 0, sizeof(num));
    int tmp = 0;
    for (int i = 1; i <= n; i++) {
      scanf("%d", a + i);
      num[a[i]]++;
      tmp = max(tmp, num[a[i]]);
    }
    int N;
    if (t >= n)
      N = n * n;
    else
      N = t * n;
    for (int j = n + 1; j <= N; j++) {
      if (j % n)
        a[j] = a[j % n];
      else
        a[j] = a[n];
    }
    int len = 0;
    for (int i = 1; i <= N; i++) {
      int pos = upper_bound(p, p + len, a[i]) - p;
      if (pos == len)
        p[len++] = a[i];
      else
        p[pos] = a[i];
    }
    int ans = len;
    if (t > n) ans = ans + (t - n) * tmp;
    printf("%d\n", ans);
  }
  return 0;
}
