#include <bits/stdc++.h>
using namespace std;
inline long long read() {
  long long s = 0, f = 1;
  char _ch = getchar();
  while (!('0' <= _ch && _ch <= '9')) (_ch == '-') && (f = -1), _ch = getchar();
  while (('0' <= _ch && _ch <= '9')) s = s * 10 + _ch - 48, _ch = getchar();
  return s * f;
}
const long long N = 4010, inf = 1e17;
long long n, m, a[N], stk[N], top, fa[N], ls[N], rs[N], sz[N];
long long f[N][N];
void dfs(long long x) {
  sz[x] = 1;
  if (ls[x]) {
    dfs(ls[x]);
    long long lm1 = min(sz[x], m), lm2;
    for (register long long i = lm1; i >= 0; i--) {
      lm2 = min(sz[ls[x]], m);
      for (register long long j = lm2; j >= 0; j--)
        f[x][i + j] =
            max(f[x][i + j],
                f[x][i] + f[ls[x]][j] + 1ll * j * (m - j) * (a[ls[x]] - a[x]));
    }
    sz[x] += sz[ls[x]];
  }
  if (rs[x]) {
    dfs(rs[x]);
    long long lm1 = min(sz[x], m), lm2;
    for (register long long i = lm1; i >= 0; i--) {
      lm2 = min(sz[rs[x]], m);
      for (register long long j = lm2; j >= 0; j--)
        f[x][i + j] =
            max(f[x][i + j],
                f[x][i] + f[rs[x]][j] + 1ll * j * (m - j) * (a[rs[x]] - a[x]));
    }
    sz[x] += sz[rs[x]];
  }
}
signed main() {
  n = read(), m = read();
  for (register long long i = 1; i <= n; i++) a[i] = read();
  for (register long long i = 1; i <= n; i++) {
    while (top && a[i] < a[stk[top]]) ls[i] = stk[top--];
    rs[stk[top]] = i;
    stk[++top] = i;
  }
  for (register long long i = 1; i <= n; i++) fa[ls[i]] = fa[rs[i]] = i;
  long long p = 1;
  for (register long long i = 1; i <= n; i++)
    if (a[i] < a[p]) p = i;
  dfs(p);
  cout << f[p][m] << '\n';
  return 0;
}

### 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;
inline long long read() {
  long long s = 0, f = 1;
  char _ch = getchar();
  while (!('0' <= _ch && _ch <= '9')) (_ch == '-') && (f = -1), _ch = getchar();
  while (('0' <= _ch && _ch <= '9')) s = s * 10 + _ch - 48, _ch = getchar();
  return s * f;
}
const long long N = 4010, inf = 1e17;
long long n, m, a[N], stk[N], top, fa[N], ls[N], rs[N], sz[N];
long long f[N][N];
void dfs(long long x) {
  sz[x] = 1;
  if (ls[x]) {
    dfs(ls[x]);
    long long lm1 = min(sz[x], m), lm2;
    for (register long long i = lm1; i >= 0; i--) {
      lm2 = min(sz[ls[x]], m);
      for (register long long j = lm2; j >= 0; j--)
        f[x][i + j] =
            max(f[x][i + j],
                f[x][i] + f[ls[x]][j] + 1ll * j * (m - j) * (a[ls[x]] - a[x]));
    }
    sz[x] += sz[ls[x]];
  }
  if (rs[x]) {
    dfs(rs[x]);
    long long lm1 = min(sz[x], m), lm2;
    for (register long long i = lm1; i >= 0; i--) {
      lm2 = min(sz[rs[x]], m);
      for (register long long j = lm2; j >= 0; j--)
        f[x][i + j] =
            max(f[x][i + j],
                f[x][i] + f[rs[x]][j] + 1ll * j * (m - j) * (a[rs[x]] - a[x]));
    }
    sz[x] += sz[rs[x]];
  }
}
signed main() {
  n = read(), m = read();
  for (register long long i = 1; i <= n; i++) a[i] = read();
  for (register long long i = 1; i <= n; i++) {
    while (top && a[i] < a[stk[top]]) ls[i] = stk[top--];
    rs[stk[top]] = i;
    stk[++top] = i;
  }
  for (register long long i = 1; i <= n; i++) fa[ls[i]] = fa[rs[i]] = i;
  long long p = 1;
  for (register long long i = 1; i <= n; i++)
    if (a[i] < a[p]) p = i;
  dfs(p);
  cout << f[p][m] << '\n';
  return 0;
}

```