#include <bits/stdc++.h>
using namespace std;
long long n, m, dsu[4069], cc[4069], dp[4069][4069], tmp[4069];
pair<long long, long long> a[4069];
long long fd(long long x) {
  if (dsu[x] != x) {
    dsu[x] = fd(dsu[x]);
  }
  return dsu[x];
}
int main() {
  long long i, j, r, u, k, l, w, z = 0;
  scanf("%lld%lld", &n, &m);
  for (i = 1; i <= n; i++) {
    scanf("%lld", &k);
    a[i] = {k, i};
  }
  sort(a + 1, a + n + 1, greater<pair<long long, long long>>());
  for (i = 1; i <= n; i++) {
    w = a[i].first;
    k = a[i].second;
    dsu[k] = k;
    cc[k] = 1;
    dp[k][1] = w * m - w;
    for (u = -1; u <= 1; u += 2) {
      if (dsu[k + u]) {
        l = fd(k + u);
        for (j = 0; j <= cc[k]; j++) {
          for (r = 0; r <= cc[l]; r++) {
            tmp[j + r] = max(tmp[j + r], dp[k][j] + dp[l][r] - w * j * r * 2);
          }
        }
        cc[k] += cc[l];
        dsu[l] = k;
        for (j = 0; j <= cc[k]; j++) {
          dp[k][j] = tmp[j];
          tmp[j] = 0;
        }
      }
    }
    z = max(z, dp[k][m]);
  }
  printf("%lld\n", z);
}

### Prompt

Generate 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;
long long n, m, dsu[4069], cc[4069], dp[4069][4069], tmp[4069];
pair<long long, long long> a[4069];
long long fd(long long x) {
  if (dsu[x] != x) {
    dsu[x] = fd(dsu[x]);
  }
  return dsu[x];
}
int main() {
  long long i, j, r, u, k, l, w, z = 0;
  scanf("%lld%lld", &n, &m);
  for (i = 1; i <= n; i++) {
    scanf("%lld", &k);
    a[i] = {k, i};
  }
  sort(a + 1, a + n + 1, greater<pair<long long, long long>>());
  for (i = 1; i <= n; i++) {
    w = a[i].first;
    k = a[i].second;
    dsu[k] = k;
    cc[k] = 1;
    dp[k][1] = w * m - w;
    for (u = -1; u <= 1; u += 2) {
      if (dsu[k + u]) {
        l = fd(k + u);
        for (j = 0; j <= cc[k]; j++) {
          for (r = 0; r <= cc[l]; r++) {
            tmp[j + r] = max(tmp[j + r], dp[k][j] + dp[l][r] - w * j * r * 2);
          }
        }
        cc[k] += cc[l];
        dsu[l] = k;
        for (j = 0; j <= cc[k]; j++) {
          dp[k][j] = tmp[j];
          tmp[j] = 0;
        }
      }
    }
    z = max(z, dp[k][m]);
  }
  printf("%lld\n", z);
}

```