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, a[100001], maxn, f[100001], l, ans = 1, b[10001];
int mm, mmm;
int main() {
  scanf("%d%d", &n, &t);
  l = min(t * n, n * n);
  for (int i = 1; i <= n; i++) {
    scanf("%d", &a[i]);
    b[a[i]]++;
    mm = max(mm, a[i]);
  }
  for (int i = n + 1; i <= l; i++) a[i] = a[i - n];
  for (int i = 1; i <= l; i++) {
    f[i] = 1;
    for (int j = max(i - n, 1); j < i; j++) {
      if (a[j] <= a[i]) f[i] = max(f[i], f[j] + 1);
    }
    ans = max(ans, f[i]);
  }
  if (t > n) {
    for (int i = 1; i <= mm; i++) mmm = max(b[i], mmm);
    ans += mmm * (t - n);
  }
  printf("%d", ans);
}
