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 dp1[10010] = {0}, dp2[10010] = {0}, dp3[310] = {0};
int a[10010];
int main() {
  int n, m;
  scanf("%d%d", &n, &m);
  for (int i = 1; i <= n; i++) {
    scanf("%d", &a[i]);
    dp3[a[i]]++;
  }
  for (int i = 1; i <= n * n; i++) {
    a[i] = a[(i - 1) % n + 1];
  }
  int l = min(n, m);
  l *= n;
  for (int i = 1; i <= l; i++) {
    int tmp = 0;
    for (int j = 0; j < i; j++)
      if (a[j] <= a[i]) tmp = max(tmp, dp1[j]);
    dp1[i] = tmp + 1;
  }
  for (int i = l; i >= 1; i--) {
    int tmp = 0;
    for (int j = l + 1; j > i; j--)
      if (a[j] >= a[i]) tmp = max(tmp, dp2[j]);
    dp2[i] = tmp + 1;
  }
  int ans = 0;
  if (m <= n) {
    for (int i = 1; i <= l; i++) {
      ans = max(ans, dp1[i] + dp2[i] - 1);
    }
  } else {
    for (int i = 1; i <= l; i++) {
      ans = max(ans, dp1[i] + dp2[i] - 1 + dp3[a[i]] * (m - n));
    }
  }
  cout << ans;
  return 0;
}
