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 long long N = 5e5;
const long long INF = 1e18;
long long n, T, i, j, i1, k, mx, cnt[N], dp[N], a[N], pos;
int main() {
  cin >> n >> T;
  for (i = 1; i <= n; ++i) {
    cin >> a[i];
    cnt[a[i]]++;
    mx = max(mx, cnt[a[i]]);
  }
  pos = n;
  for (i = 1; i < min(T, n); ++i)
    for (j = 1; j <= n; ++j) a[++pos] = a[j];
  dp[0] = -INF;
  for (i = 1; i <= pos; ++i) dp[i] = INF;
  for (i = 1; i <= pos; ++i) {
    i1 = upper_bound(dp, dp + pos, a[i]) - dp;
    if (dp[i1 - 1] <= a[i] && a[i] <= dp[i1]) dp[i1] = a[i];
  }
  for (i = 0; i <= pos; ++i)
    if (dp[i] != 1e18) k = i;
  if (T <= n) return cout << k, 0;
  return cout << k + (T - n) * mx, 0;
}
