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 maxn = 110;
int a[maxn], T, n;
int dp[3][310];
int co[310];
int main() {
  scanf("%d%d", &n, &T);
  for (int i = 1; i <= n; i++) scanf("%d", &a[i]);
  int ret = 0;
  int now = 1, nxt = 0;
  int turn = min(T, 300);
  if (T - turn <= 300) turn = T;
  memset(dp, 0, sizeof(dp));
  for (int i = 1; i <= turn; i++) {
    for (int j = 1; j <= n; j++) {
      swap(now, nxt);
      memset(dp[nxt], 0, sizeof(dp[nxt]));
      for (int k = 0; k <= a[j]; k++)
        dp[nxt][a[j]] = max(dp[nxt][a[j]], dp[now][k] + 1);
      for (int k = 0; k <= 300; k++)
        if (k != a[j]) dp[nxt][k] = dp[now][k];
    }
  }
  for (int i = 1; i <= 300; i++) ret = max(ret, dp[nxt][i]);
  if (turn == T) {
    printf("%d\n", ret);
    return 0;
  }
  memset(co, 0, sizeof(co));
  for (int i = 1; i <= n; i++) co[a[i]]++;
  for (int i = 0; i <= 300; i++) dp[nxt][i] += (T - turn - 300) * co[i];
  for (int i = 1; i <= 300; i++) {
    for (int j = 1; j <= n; j++) {
      swap(now, nxt);
      memset(dp[nxt], 0, sizeof(dp[nxt]));
      for (int k = 0; k <= a[j]; k++)
        dp[nxt][a[j]] = max(dp[nxt][a[j]], dp[now][k] + 1);
      for (int k = 0; k <= 300; k++)
        if (k != a[j]) dp[nxt][k] = dp[now][k];
    }
  }
  for (int i = 1; i <= 300; i++) ret = max(ret, dp[nxt][i]);
  printf("%d\n", ret);
}
