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 M = 305;
int n, t, ans;
int a[M * M], d1[M * M], d2[M * M], m[M], num[M];
int main() {
  scanf("%d%d", &n, &t);
  for (int i = 1; i <= n; i++) {
    scanf("%d", &a[i]);
    num[a[i]]++;
  }
  for (int k = 1; k <= min(t, n); k++) {
    for (int i = 1; i <= n; i++) a[i + (k - 1) * n] = a[i];
    int e = n * k + 1;
    a[e] = 1000000000;
    memset(m, 0, sizeof(m));
    memset(d1, 0, sizeof(d1));
    memset(d2, 0, sizeof(d2));
    for (int i = 1; i < e; i++) {
      for (int j = 1; j <= a[i]; j++) d1[i] = max(d1[i], m[j] + 1);
      m[a[i]] = d1[i];
    }
    memset(m, 0, sizeof(m));
    for (int i = e - 1; i >= 1; i--) {
      for (int j = 300; j >= a[i]; j--) d2[i] = max(d2[i], m[j] + 1);
      m[a[i]] = d2[i];
    }
    for (int i = 1; i < e; i++)
      ans = max(ans, d1[i] + d2[i] - 1 + (t - k) * num[a[i]]);
  }
  printf("%d", ans);
  return 0;
}
