#include <bits/stdc++.h>
using namespace std;
int N, M;
int A[4040];
vector<long long> ret;
void calc(int L, int R) {
  if (R - L == 0) {
    ret.clear();
    ret.push_back(0);
    return;
  }
  int mid = L;
  for (int i = L + 1; i < R; i++)
    if (A[mid] > A[i]) mid = i;
  vector<long long> l, r;
  calc(L, mid);
  l.swap(ret);
  calc(mid + 1, R);
  r.swap(ret);
  ret.clear();
  ret.assign(l.size() + r.size(), -(long long)1e18);
  for (int i = 0; i < l.size(); i++)
    for (int j = 0; j < r.size(); j++) {
      ret[i + j] = max(ret[i + j], l[i] + r[j] - (long long)A[mid] * i * j * 2);
    }
  for (int i = ret.size() - 2; i >= 0; i--)
    ret[i + 1] = max(ret[i + 1], ret[i] + (long long)(M - 1 - 2 * i) * A[mid]);
}
int main() {
  cin >> N >> M;
  for (int i = 0; i < N; i++) cin >> A[i];
  calc(0, N);
  cout << ret[M] << endl;
}

### Prompt

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

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;
int N, M;
int A[4040];
vector<long long> ret;
void calc(int L, int R) {
  if (R - L == 0) {
    ret.clear();
    ret.push_back(0);
    return;
  }
  int mid = L;
  for (int i = L + 1; i < R; i++)
    if (A[mid] > A[i]) mid = i;
  vector<long long> l, r;
  calc(L, mid);
  l.swap(ret);
  calc(mid + 1, R);
  r.swap(ret);
  ret.clear();
  ret.assign(l.size() + r.size(), -(long long)1e18);
  for (int i = 0; i < l.size(); i++)
    for (int j = 0; j < r.size(); j++) {
      ret[i + j] = max(ret[i + j], l[i] + r[j] - (long long)A[mid] * i * j * 2);
    }
  for (int i = ret.size() - 2; i >= 0; i--)
    ret[i + 1] = max(ret[i + 1], ret[i] + (long long)(M - 1 - 2 * i) * A[mid]);
}
int main() {
  cin >> N >> M;
  for (int i = 0; i < N; i++) cin >> A[i];
  calc(0, N);
  cout << ret[M] << endl;
}

```