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 dp[MAXN];
int num[MAXN], a[110];
int re[330], val;
int main() {
  int n, t;
  int maxncnt = 0;
  memset(re, 0, sizeof(re));
  memset(dp, 0, sizeof(dp));
  scanf("%d%d", &n, &t);
  for (int i = 0; i < n; i++) {
    scanf("%d", &a[i]);
    re[a[i]]++;
    if (re[a[i]] > maxncnt) maxncnt = re[a[i]];
  }
  int cnt = 0;
  for (int i = 0; i < min(n, t); i++) {
    for (int j = 0; j < n; j++) {
      num[cnt++] = a[j];
    }
  }
  int val = 1;
  dp[0] = num[0];
  for (int i = 1; i < cnt; i++) {
    if (num[i] >= dp[val - 1])
      dp[val++] = num[i];
    else {
      int pos = upper_bound(dp, dp + val, num[i]) - dp;
      dp[pos] = num[i];
    }
  }
  if (t > n) val += (t - n) * maxncnt;
  printf("%d\n", val);
  return 0;
}
