#include <bits/stdc++.h>
using namespace std;
long long read() {
  long long f = 0, s = 0;
  char c = getchar();
  while (c > '9' || c < '0') f = (c == '-'), c = getchar();
  while (c >= '0' && c <= '9')
    s = (s << 3) + (s << 1) + (c ^ '0'), c = getchar();
  return f ? -s : s;
}
const long long N = 4005;
long long n, m;
long long a[N];
long long rt;
long long c[N][2];
long long st[N], tp = 0;
long long f[N][N];
long long siz[N];
void dfs(long long u) {
  if (c[u][0]) dfs(c[u][0]);
  if (c[u][1]) dfs(c[u][1]);
  siz[u] = 1;
  if (c[u][0]) {
    long long lw = a[c[u][0]] - a[u];
    for (long long i = siz[u]; i >= 0; i--)
      for (long long j = 0; j <= siz[c[u][0]]; j++)
        f[u][i + j] =
            max(f[u][i + j], f[u][i] + f[c[u][0]][j] + j * (m - j) * lw);
    siz[u] += siz[c[u][0]];
  }
  if (c[u][1]) {
    long long rw = a[c[u][1]] - a[u];
    for (long long i = siz[u]; i >= 0; i--)
      for (long long j = 0; j <= siz[c[u][1]]; j++)
        f[u][i + j] =
            max(f[u][i + j], f[u][i] + f[c[u][1]][j] + j * (m - j) * rw);
    siz[u] += siz[c[u][1]];
  }
}
long long ans = 0;
signed main() {
  n = read();
  m = read();
  for (long long i = 1; i <= n; i++) a[i] = read();
  for (long long i = 1; i <= n; i++) {
    long long now = tp;
    while (now && a[i] < a[st[now]]) now--;
    if (now != tp) c[i][0] = st[now + 1];
    if (now) c[st[now]][1] = i;
    tp = now;
    st[++tp] = i;
  }
  for (long long i = 1; i < tp; i++) c[st[i]][1] = st[i + 1];
  rt = st[1];
  memset(f, 0, sizeof f);
  dfs(rt);
  printf("%lld", f[rt][m]);
  return 0;
}

### Prompt

Please formulate 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 read() {
  long long f = 0, s = 0;
  char c = getchar();
  while (c > '9' || c < '0') f = (c == '-'), c = getchar();
  while (c >= '0' && c <= '9')
    s = (s << 3) + (s << 1) + (c ^ '0'), c = getchar();
  return f ? -s : s;
}
const long long N = 4005;
long long n, m;
long long a[N];
long long rt;
long long c[N][2];
long long st[N], tp = 0;
long long f[N][N];
long long siz[N];
void dfs(long long u) {
  if (c[u][0]) dfs(c[u][0]);
  if (c[u][1]) dfs(c[u][1]);
  siz[u] = 1;
  if (c[u][0]) {
    long long lw = a[c[u][0]] - a[u];
    for (long long i = siz[u]; i >= 0; i--)
      for (long long j = 0; j <= siz[c[u][0]]; j++)
        f[u][i + j] =
            max(f[u][i + j], f[u][i] + f[c[u][0]][j] + j * (m - j) * lw);
    siz[u] += siz[c[u][0]];
  }
  if (c[u][1]) {
    long long rw = a[c[u][1]] - a[u];
    for (long long i = siz[u]; i >= 0; i--)
      for (long long j = 0; j <= siz[c[u][1]]; j++)
        f[u][i + j] =
            max(f[u][i + j], f[u][i] + f[c[u][1]][j] + j * (m - j) * rw);
    siz[u] += siz[c[u][1]];
  }
}
long long ans = 0;
signed main() {
  n = read();
  m = read();
  for (long long i = 1; i <= n; i++) a[i] = read();
  for (long long i = 1; i <= n; i++) {
    long long now = tp;
    while (now && a[i] < a[st[now]]) now--;
    if (now != tp) c[i][0] = st[now + 1];
    if (now) c[st[now]][1] = i;
    tp = now;
    st[++tp] = i;
  }
  for (long long i = 1; i < tp; i++) c[st[i]][1] = st[i + 1];
  rt = st[1];
  memset(f, 0, sizeof f);
  dfs(rt);
  printf("%lld", f[rt][m]);
  return 0;
}

```