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 MX = 50;
const int MAXN = 120000;
int dp[400];
int cnt[400];
int a[MAXN];
int n, t;
int main() {
  cin >> n >> t;
  for (int i = 0; i < n; ++i) cin >> a[i], ++cnt[a[i]];
  int p = 0;
  for (int i = 0; i <= 300; ++i) p = max(p, cnt[i]);
  int k = min(t, MX);
  for (int i = n; i < n * k; ++i) a[i] = a[i - n];
  for (int i = 0; i < n * k; ++i) {
    dp[a[i]] += 1;
    for (int j = a[i] - 1; j >= 0; --j) dp[a[i]] = max(dp[a[i]], dp[j] + 1);
  }
  int mx = 0;
  for (int i = 0; i <= 300; ++i) mx = max(mx, dp[i]);
  mx += (t - k) * p;
  cout << mx;
  return 0;
}
