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 v[110 * 110];
int n, t;
vector<int> dp;
int tam;
int cnt[400];
void lis() {
  dp.push_back(v[0]);
  for (int i = 1; i < n * tam; ++i) {
    if (v[i] >= dp.back())
      dp.push_back(v[i]);
    else {
      int pos = upper_bound(dp.begin(), dp.end(), v[i]) - dp.begin();
      dp[pos] = v[i];
    }
  }
}
int main(void) {
  cin >> n >> t;
  int maior = 0;
  for (int i = 0; i < n; ++i) {
    cin >> v[i];
    cnt[v[i]]++;
    maior = max(maior, cnt[v[i]]);
  }
  tam = min(n, t);
  for (int i = n; i < n * tam; ++i) {
    v[i] = v[i - n];
  }
  lis();
  cout << dp.size() + maior * (t - tam) << "\n";
  return 0;
}
