#include <bits/stdc++.h>
using namespace std;
long long a[4005], v[4005 * 2];
int m;
vector<long long> f[4005 * 2];
int cnt[4005 * 2], tot;
int son[4005 * 2][2];
void Max(long long &x, long long y) {
  if (y > x) x = y;
}
void solve(int l, int r, int &rt) {
  rt = ++tot;
  f[rt].push_back(0);
  for (int i = l; i <= r; i++) f[rt].push_back(0);
  if (l > r) {
    return;
  }
  if (l == r) {
    v[rt] = a[l];
    cnt[rt] = 1;
    return;
  }
  int mx = a[l], id = l;
  for (int i = l; i <= r; i++) {
    if (a[i] < mx) {
      id = i;
      mx = a[i];
    }
  }
  v[rt] = mx;
  solve(l, id - 1, son[rt][0]);
  solve(id + 1, r, son[rt][1]);
  for (int i = 0; i <= cnt[son[rt][0]]; i++) {
    for (int j = 0; j <= cnt[son[rt][1]]; j++) {
      Max(f[rt][i + j],
          f[son[rt][0]][i] + (v[son[rt][0]] - v[rt]) * (i) * (m - i) +
              f[son[rt][1]][j] + (v[son[rt][1]] - v[rt]) * j * (m - j));
      Max(f[rt][i + j + 1],
          f[son[rt][0]][i] + (v[son[rt][0]] - v[rt]) * (i) * (m - i) +
              f[son[rt][1]][j] + (v[son[rt][1]] - v[rt]) * j * (m - j));
    }
  }
  cnt[rt] = cnt[son[rt][0]] + cnt[son[rt][1]] + 1;
}
int main() {
  int n;
  scanf("%d%d", &n, &m);
  for (int i = 1; i <= n; i++) {
    scanf("%lld", &a[i]);
  }
  int rt = 0;
  solve(1, n, rt);
  printf("%lld\n", f[rt][m]);
  return 0;
}

### Prompt

In Cpp, your task is to solve 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 a[4005], v[4005 * 2];
int m;
vector<long long> f[4005 * 2];
int cnt[4005 * 2], tot;
int son[4005 * 2][2];
void Max(long long &x, long long y) {
  if (y > x) x = y;
}
void solve(int l, int r, int &rt) {
  rt = ++tot;
  f[rt].push_back(0);
  for (int i = l; i <= r; i++) f[rt].push_back(0);
  if (l > r) {
    return;
  }
  if (l == r) {
    v[rt] = a[l];
    cnt[rt] = 1;
    return;
  }
  int mx = a[l], id = l;
  for (int i = l; i <= r; i++) {
    if (a[i] < mx) {
      id = i;
      mx = a[i];
    }
  }
  v[rt] = mx;
  solve(l, id - 1, son[rt][0]);
  solve(id + 1, r, son[rt][1]);
  for (int i = 0; i <= cnt[son[rt][0]]; i++) {
    for (int j = 0; j <= cnt[son[rt][1]]; j++) {
      Max(f[rt][i + j],
          f[son[rt][0]][i] + (v[son[rt][0]] - v[rt]) * (i) * (m - i) +
              f[son[rt][1]][j] + (v[son[rt][1]] - v[rt]) * j * (m - j));
      Max(f[rt][i + j + 1],
          f[son[rt][0]][i] + (v[son[rt][0]] - v[rt]) * (i) * (m - i) +
              f[son[rt][1]][j] + (v[son[rt][1]] - v[rt]) * j * (m - j));
    }
  }
  cnt[rt] = cnt[son[rt][0]] + cnt[son[rt][1]] + 1;
}
int main() {
  int n;
  scanf("%d%d", &n, &m);
  for (int i = 1; i <= n; i++) {
    scanf("%lld", &a[i]);
  }
  int rt = 0;
  solve(1, n, rt);
  printf("%lld\n", f[rt][m]);
  return 0;
}

```