#include <bits/stdc++.h>
using namespace std;
inline long long read() {
  char ch = getchar();
  long long nega = 1;
  while (!isdigit(ch)) {
    if (ch == '-') nega = -1;
    ch = getchar();
  }
  long long ans = 0;
  while (isdigit(ch)) {
    ans = ans * 10 + ch - 48;
    ch = getchar();
  }
  if (nega == -1) return -ans;
  return ans;
}
void print(vector<long long> x) {
  for (long long i = 0; i < (long long)x.size(); i++)
    printf("%lld%c", x[i], " \n"[i == (long long)x.size() - 1]);
}
long long a[4005], n, m;
long long val[4005], f[4005][4005], vis[4005];
signed main() {
  cin >> n >> m;
  for (long long i = 1; i <= n; i++) a[i] = read();
  for (long long i = 1; i <= n; i++) {
    f[i][i] = a[i];
    for (long long j = i + 1; j <= n; j++) f[i][j] = min(f[i][j - 1], a[j]);
  }
  long long ans = 0;
  for (long long i = 1; i <= m; i++) {
    long long maxn = -0x3f3f3f3f3f3f3f3f, maxid = 0;
    for (long long j = 1; j <= n; j++)
      if (!vis[j]) {
        long long w = val[j] * 2 + (m - 1) * a[j];
        if (w > maxn) maxn = w, maxid = j;
      }
    vis[maxid] = 1;
    ans += maxn;
    for (long long i = 1; i < maxid; i++) val[i] -= f[i][maxid];
    for (long long i = maxid + 1; i <= n; i++) val[i] -= f[maxid][i];
  }
  cout << ans << endl;
  return 0;
}

### Prompt

Please formulate a cpp solution to the following problem:

Alice has an integer sequence a of length n and all elements are different. She will choose a subsequence of a of length m, and defines the value of a subsequence a_{b_1},a_{b_2},…,a_{b_m} as $$$∑_{i = 1}^m (m ⋅ a_{b_i}) - ∑_{i = 1}^m ∑_{j = 1}^m f(min(b_i, b_j), max(b_i, b_j)), where f(i, j) denotes \min(a_i, a_{i + 1}, \ldots, a_j)$$$.

Alice wants you to help her to maximize the value of the subsequence she choose.

A sequence s is a subsequence of a sequence t if s can be obtained from t by deletion of several (possibly, zero or all) elements.

Input

The first line contains two integers n and m (1 ≤ m ≤ n ≤ 4000).

The second line contains n distinct integers a_1, a_2, …, a_n (1 ≤ a_i < 2^{31}).

Output

Print the maximal value Alice can get.

Examples

Input


6 4
15 2 18 12 13 4


Output


100


Input


11 5
9 3 7 1 8 12 10 20 15 18 5


Output


176


Input


1 1
114514


Output


0


Input


2 1
666 888


Output


0

Note

In the first example, Alice can choose the subsequence [15, 2, 18, 13], which has the value 4 ⋅ (15 + 2 + 18 + 13) - (15 + 2 + 2 + 2) - (2 + 2 + 2 + 2) - (2 + 2 + 18 + 12) - (2 + 2 + 12 + 13) = 100. In the second example, there are a variety of subsequences with value 176, and one of them is [9, 7, 12, 20, 18].

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
inline long long read() {
  char ch = getchar();
  long long nega = 1;
  while (!isdigit(ch)) {
    if (ch == '-') nega = -1;
    ch = getchar();
  }
  long long ans = 0;
  while (isdigit(ch)) {
    ans = ans * 10 + ch - 48;
    ch = getchar();
  }
  if (nega == -1) return -ans;
  return ans;
}
void print(vector<long long> x) {
  for (long long i = 0; i < (long long)x.size(); i++)
    printf("%lld%c", x[i], " \n"[i == (long long)x.size() - 1]);
}
long long a[4005], n, m;
long long val[4005], f[4005][4005], vis[4005];
signed main() {
  cin >> n >> m;
  for (long long i = 1; i <= n; i++) a[i] = read();
  for (long long i = 1; i <= n; i++) {
    f[i][i] = a[i];
    for (long long j = i + 1; j <= n; j++) f[i][j] = min(f[i][j - 1], a[j]);
  }
  long long ans = 0;
  for (long long i = 1; i <= m; i++) {
    long long maxn = -0x3f3f3f3f3f3f3f3f, maxid = 0;
    for (long long j = 1; j <= n; j++)
      if (!vis[j]) {
        long long w = val[j] * 2 + (m - 1) * a[j];
        if (w > maxn) maxn = w, maxid = j;
      }
    vis[maxid] = 1;
    ans += maxn;
    for (long long i = 1; i < maxid; i++) val[i] -= f[i][maxid];
    for (long long i = maxid + 1; i <= n; i++) val[i] -= f[maxid][i];
  }
  cout << ans << endl;
  return 0;
}

```