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;
int a[30005], num[305];
int stk[30005];
int main() {
  scanf("%d %d", &n, &T);
  int ma = 0;
  for (int i = 0; i < n; i++) {
    scanf("%d", &a[i]);
    num[a[i]]++;
    ma = max(ma, num[a[i]]);
  }
  int ans = 0, len = min(300, n), top = 0;
  for (int i = n; i < n * len; i++) a[i] = a[i - n];
  for (int i = 0; i < n * len; i++) {
    if (a[i] >= stk[top])
      stk[++top] = a[i];
    else {
      int pos = upper_bound(stk, stk + top + 1, a[i]) - stk;
      stk[pos] = a[i];
    }
    ans = max(ans, top);
  }
  printf("%d\n", ans + (T - len) * ma);
}
