#include <bits/stdc++.h>
using namespace std;
const long long mod = 1e9 + 7;
int a[100005];
int dp[100005];
int cnt[100005];
int id[100005];
int main(void) {
  int n, m;
  scanf("%d %d", &n, &m);
  for (int i = 0; i < n; i++) scanf("%d", &a[i]);
  int maxx = 1;
  if (m <= 100) {
    for (int i = n; i < n * m; i++) {
      a[i] = a[i - n];
    }
    dp[0] = 1;
    for (int i = 1; i < n * m; i++) {
      dp[i] = 1;
      for (int j = 0; j < i; j++) {
        if (a[i] >= a[j]) dp[i] = max(dp[j] + 1, dp[i]);
      }
      maxx = max(maxx, dp[i]);
    }
  } else {
    for (int i = n; i < n * 100; i++) a[i] = a[i - n];
    for (int i = 0; i < n; i++) cnt[a[i]]++;
    dp[0] = 1;
    for (int i = 1; i < n * 100; i++) {
      dp[i] = 1;
      for (int j = 0; j < i; j++) {
        if (a[i] >= a[j]) {
          if (dp[i] < dp[j] + 1) {
            dp[i] = dp[j] + 1;
            id[i] = j;
          }
        }
      }
      int c = i;
      while (c != 0) maxx = max(maxx, dp[i] + (m - 100) * cnt[a[c]]), c = id[c];
    }
  }
  printf("%d\n", maxx);
  return 0;
}

### Prompt

Please provide a cpp coded solution to the problem described below:

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. 

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
const long long mod = 1e9 + 7;
int a[100005];
int dp[100005];
int cnt[100005];
int id[100005];
int main(void) {
  int n, m;
  scanf("%d %d", &n, &m);
  for (int i = 0; i < n; i++) scanf("%d", &a[i]);
  int maxx = 1;
  if (m <= 100) {
    for (int i = n; i < n * m; i++) {
      a[i] = a[i - n];
    }
    dp[0] = 1;
    for (int i = 1; i < n * m; i++) {
      dp[i] = 1;
      for (int j = 0; j < i; j++) {
        if (a[i] >= a[j]) dp[i] = max(dp[j] + 1, dp[i]);
      }
      maxx = max(maxx, dp[i]);
    }
  } else {
    for (int i = n; i < n * 100; i++) a[i] = a[i - n];
    for (int i = 0; i < n; i++) cnt[a[i]]++;
    dp[0] = 1;
    for (int i = 1; i < n * 100; i++) {
      dp[i] = 1;
      for (int j = 0; j < i; j++) {
        if (a[i] >= a[j]) {
          if (dp[i] < dp[j] + 1) {
            dp[i] = dp[j] + 1;
            id[i] = j;
          }
        }
      }
      int c = i;
      while (c != 0) maxx = max(maxx, dp[i] + (m - 100) * cnt[a[c]]), c = id[c];
    }
  }
  printf("%d\n", maxx);
  return 0;
}

```