#include <bits/stdc++.h>
const long long mod = 998244353;
long long Add(long long x, long long y) {
  return (x + y >= mod) ? (x + y - mod) : (x + y);
}
long long Mul(long long x, long long y) { return x * y % mod; }
long long Mod(long long x) {
  return x < 0 ? (x + mod) : (x >= mod ? (x - mod) : x);
}
long long cadd(long long &x, long long y) {
  return x = (x + y >= mod) ? (x + y - mod) : (x + y);
}
template <typename T>
T Max(T x, T y) {
  return x > y ? x : y;
}
template <typename T>
T Min(T x, T y) {
  return x < y ? x : y;
}
template <typename T>
T &read(T &r) {
  r = 0;
  bool w = 0;
  char ch = getchar();
  while (ch < '0' || ch > '9') w = ch == '-' ? 1 : 0, ch = getchar();
  while (ch >= '0' && ch <= '9') r = r * 10 + (ch ^ 48), ch = getchar();
  return r = w ? -r : r;
}
const long long N = 4010;
long long n, m, ls[N], rs[N], st[N], top, a[N], siz[N];
long long f[N][N];
std::vector<long long> eg[N];
void dfs(long long x) {
  siz[x] = 1;
  for (auto v : eg[x]) dfs(v);
  if (eg[x].size() == 0) {
    f[x][1] = 1ll * (m - 1) * a[x];
    return;
  }
  for (auto v : eg[x]) {
    for (long long j = siz[x] + siz[v]; j >= 0; --j)
      for (long long k = Max(0ll, j - siz[x]); k <= Min(j, siz[v]); ++k)
        f[x][j] =
            Max(f[x][j], f[v][k] + f[x][j - k] - 2ll * k * (j - k) * a[x]);
    siz[x] += siz[v];
  }
  for (long long j = siz[x]; j; --j)
    f[x][j] =
        Max(f[x][j], f[x][j - 1] + 1ll * (m - 1) * a[x] - 2ll * (j - 1) * a[x]);
}
signed main() {
  read(n);
  read(m);
  for (long long i = 1; i <= n; ++i)
    for (long long j = 1; j <= m; ++j) f[i][j] = -0x3f3f3f3f3f3f3f3f;
  for (long long i = 1; i <= n; ++i) {
    read(a[i]);
    long long k = top;
    while (k && a[st[k]] > a[i]) --k;
    if (k) rs[st[k]] = i;
    if (k < top) ls[i] = st[k + 1];
    st[top = k + 1] = i;
  }
  for (long long i = 1; i <= n; ++i) {
    if (ls[i]) eg[i].emplace_back(ls[i]);
    if (rs[i]) eg[i].emplace_back(rs[i]);
  }
  dfs(st[1]);
  printf("%lld\n", f[st[1]][m]);
  return 0;
}

### Prompt

Create a solution in CPP for 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>
const long long mod = 998244353;
long long Add(long long x, long long y) {
  return (x + y >= mod) ? (x + y - mod) : (x + y);
}
long long Mul(long long x, long long y) { return x * y % mod; }
long long Mod(long long x) {
  return x < 0 ? (x + mod) : (x >= mod ? (x - mod) : x);
}
long long cadd(long long &x, long long y) {
  return x = (x + y >= mod) ? (x + y - mod) : (x + y);
}
template <typename T>
T Max(T x, T y) {
  return x > y ? x : y;
}
template <typename T>
T Min(T x, T y) {
  return x < y ? x : y;
}
template <typename T>
T &read(T &r) {
  r = 0;
  bool w = 0;
  char ch = getchar();
  while (ch < '0' || ch > '9') w = ch == '-' ? 1 : 0, ch = getchar();
  while (ch >= '0' && ch <= '9') r = r * 10 + (ch ^ 48), ch = getchar();
  return r = w ? -r : r;
}
const long long N = 4010;
long long n, m, ls[N], rs[N], st[N], top, a[N], siz[N];
long long f[N][N];
std::vector<long long> eg[N];
void dfs(long long x) {
  siz[x] = 1;
  for (auto v : eg[x]) dfs(v);
  if (eg[x].size() == 0) {
    f[x][1] = 1ll * (m - 1) * a[x];
    return;
  }
  for (auto v : eg[x]) {
    for (long long j = siz[x] + siz[v]; j >= 0; --j)
      for (long long k = Max(0ll, j - siz[x]); k <= Min(j, siz[v]); ++k)
        f[x][j] =
            Max(f[x][j], f[v][k] + f[x][j - k] - 2ll * k * (j - k) * a[x]);
    siz[x] += siz[v];
  }
  for (long long j = siz[x]; j; --j)
    f[x][j] =
        Max(f[x][j], f[x][j - 1] + 1ll * (m - 1) * a[x] - 2ll * (j - 1) * a[x]);
}
signed main() {
  read(n);
  read(m);
  for (long long i = 1; i <= n; ++i)
    for (long long j = 1; j <= m; ++j) f[i][j] = -0x3f3f3f3f3f3f3f3f;
  for (long long i = 1; i <= n; ++i) {
    read(a[i]);
    long long k = top;
    while (k && a[st[k]] > a[i]) --k;
    if (k) rs[st[k]] = i;
    if (k < top) ls[i] = st[k + 1];
    st[top = k + 1] = i;
  }
  for (long long i = 1; i <= n; ++i) {
    if (ls[i]) eg[i].emplace_back(ls[i]);
    if (rs[i]) eg[i].emplace_back(rs[i]);
  }
  dfs(st[1]);
  printf("%lld\n", f[st[1]][m]);
  return 0;
}

```