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 A[101], C[301], n, DP[101 * 101], p, ans, mx;
int main() {
  scanf("%d %d", &n, &p);
  for (int i = 0; i < n; ++i) scanf("%d", A + i);
  for (int i = 0; i < n * min(n, p); ++i) {
    DP[i] = 1;
    for (int j = 0; j < i; ++j) {
      if (A[j % n] <= A[i % n]) DP[i] = max(DP[i], DP[j] + 1);
    }
    ans = max(ans, DP[i]);
  }
  for (int i = 0; i < n; ++i) {
    C[A[i]]++;
    mx = max(mx, C[A[i]]);
  }
  printf("%d", ans + (p > n ? (p - n) * mx : 0));
}
