#include <bits/stdc++.h>
using namespace std;
const long long N = 4e3 + 5;
long long n, m, a[N], f[N][N];
long long solve(long long l, long long r) {
  if (l > r) return 0;
  long long p = 0;
  for (long long i = l; i <= r; i++)
    if (a[i] < a[p]) p = i;
  long long ls = solve(l, p - 1), rs = solve(p + 1, r);
  memset(f[p], -0x3f, sizeof(f[p]));
  for (long long i = 0; i <= p - l; i++)
    for (long long j = 0; j <= r - p; j++) {
      f[p][i + j] = max(f[p][i + j], f[ls][i] + f[rs][j] - 2 * i * j * a[p]);
      f[p][i + j + 1] =
          max(f[p][i + j + 1], f[ls][i] + f[rs][j] - 2 * i * j * a[p] -
                                   2 * (i + j) * a[p] + (m - 1) * a[p]);
    }
  return p;
}
signed main() {
  cin >> n >> m;
  a[0] = 1e18;
  for (long long i = 1; i <= n; i++) cin >> a[i];
  long long p = solve(1, n);
  cout << f[p][m] << endl;
}

### Prompt

Your task is to create 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;
const long long N = 4e3 + 5;
long long n, m, a[N], f[N][N];
long long solve(long long l, long long r) {
  if (l > r) return 0;
  long long p = 0;
  for (long long i = l; i <= r; i++)
    if (a[i] < a[p]) p = i;
  long long ls = solve(l, p - 1), rs = solve(p + 1, r);
  memset(f[p], -0x3f, sizeof(f[p]));
  for (long long i = 0; i <= p - l; i++)
    for (long long j = 0; j <= r - p; j++) {
      f[p][i + j] = max(f[p][i + j], f[ls][i] + f[rs][j] - 2 * i * j * a[p]);
      f[p][i + j + 1] =
          max(f[p][i + j + 1], f[ls][i] + f[rs][j] - 2 * i * j * a[p] -
                                   2 * (i + j) * a[p] + (m - 1) * a[p]);
    }
  return p;
}
signed main() {
  cin >> n >> m;
  a[0] = 1e18;
  for (long long i = 1; i <= n; i++) cin >> a[i];
  long long p = solve(1, n);
  cout << f[p][m] << endl;
}

```