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[20000], num[20000];
int dp[400];
int n, m, t, k, ans, maxm;
int main() {
  scanf("%d%d", &n, &m);
  maxm = 0;
  ans = 0;
  for (int i = 1; i <= n; i++) {
    scanf("%d", &a[i]);
    num[a[i]]++;
    maxm = max(maxm, num[a[i]]);
  }
  t = min(n, m);
  k = t;
  int temp = 0;
  while (--k) {
    temp += n;
    for (int i = 1; i <= n; i++) a[temp + i] = a[i];
  }
  for (int i = 1; i <= n * t; i++) {
    dp[a[i]]++;
    for (int j = a[i] - 1; j >= 0; j--) dp[a[i]] = max(dp[a[i]], dp[j] + 1);
    ans = max(dp[a[i]], ans);
  }
  ans += maxm * (m - t);
  printf("%d\n", ans);
  return 0;
}
