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 LIS(int a[], int n) {
  int i, j;
  int dp[10005];
  int relset;
  dp[0] = 1;
  relset = 1;
  for (i = 1; i < n; i++) {
    dp[i] = 1;
    for (j = 0; j < i; j++) {
      if (a[i] >= a[j]) dp[i] = max(dp[j] + 1, dp[i]);
    }
    relset = max(relset, dp[i]);
  }
  return relset;
}
int fuck[305];
int main() {
  int n, T;
  int a[100005];
  scanf("%d %d", &n, &T);
  memset(fuck, 0, sizeof(fuck));
  for (int i = 0; i < n; i++) {
    scanf("%d", &a[i]);
    fuck[a[i]]++;
  }
  int maxsame = 0;
  for (int i = 0; i < 307; i++) maxsame = max(fuck[i], maxsame);
  int b[10005];
  int len;
  if (T <= n)
    len = T * n;
  else
    len = n * n;
  for (int i = n; i < len; i++) a[i] = a[i - n];
  int out = LIS(a, len);
  if (T > n) {
    out = out + maxsame * (T - n);
  }
  printf("%d\n", out);
}
