#include <bits/stdc++.h>
using namespace std;
template <typename T1, typename T2>
void CMax(T1 &x, T2 y) {
  if (y > x) x = y;
}
template <typename T1, typename T2>
void CMin(T1 &x, T2 y) {
  if (y < x) x = y;
}
template <typename T>
void read(T &x) {
  x = 0;
  int op = 1;
  char c = getchar();
  while (!isdigit(c)) {
    if (c == '-') op = -1;
    c = getchar();
  }
  while (isdigit(c)) {
    x = (x << 1) + (x << 3) + (c ^ 48);
    c = getchar();
  }
  x *= op;
}
inline void swap(int &x, int &y) { x ^= y ^= x ^= y; }
inline int max(int x, int y) { return x > y ? x : y; }
inline int min(int x, int y) { return x < y ? x : y; }
const int MN = 4005;
int n, m, a[MN];
int stk[MN], top;
int ls[MN], rs[MN];
int sz[MN];
long long dp[MN][MN];
void DP(int x) {
  sz[x] = 1;
  if (ls[x]) {
    DP(ls[x]);
    int w = a[ls[x]] - a[x];
    for (int i = min(m, sz[x]); ~i; --i)
      for (int j = min(m, sz[ls[x]]); ~j; --j)
        dp[x][i + j] =
            max(dp[x][i + j], dp[x][i] + dp[ls[x]][j] + 1ll * w * (m - j) * j);
    sz[x] += sz[ls[x]];
  }
  if (rs[x]) {
    DP(rs[x]);
    int w = a[rs[x]] - a[x];
    for (int i = min(m, sz[x]); ~i; --i)
      for (int j = min(m, sz[rs[x]]); ~j; --j)
        dp[x][i + j] =
            max(dp[x][i + j], dp[x][i] + dp[rs[x]][j] + 1ll * w * (m - j) * j);
    sz[x] += sz[rs[x]];
  }
}
int main() {
  read(n);
  read(m);
  for (int i = (1); i <= (n); ++i) read(a[i]);
  for (int i = 1; i <= n; ++i) {
    while (top && a[stk[top]] > a[i]) top--;
    if (!top)
      ls[i] = stk[1];
    else
      ls[i] = rs[stk[top]], rs[stk[top]] = i;
    stk[++top] = i;
  }
  DP(stk[1]);
  printf("%lld", dp[stk[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>
using namespace std;
template <typename T1, typename T2>
void CMax(T1 &x, T2 y) {
  if (y > x) x = y;
}
template <typename T1, typename T2>
void CMin(T1 &x, T2 y) {
  if (y < x) x = y;
}
template <typename T>
void read(T &x) {
  x = 0;
  int op = 1;
  char c = getchar();
  while (!isdigit(c)) {
    if (c == '-') op = -1;
    c = getchar();
  }
  while (isdigit(c)) {
    x = (x << 1) + (x << 3) + (c ^ 48);
    c = getchar();
  }
  x *= op;
}
inline void swap(int &x, int &y) { x ^= y ^= x ^= y; }
inline int max(int x, int y) { return x > y ? x : y; }
inline int min(int x, int y) { return x < y ? x : y; }
const int MN = 4005;
int n, m, a[MN];
int stk[MN], top;
int ls[MN], rs[MN];
int sz[MN];
long long dp[MN][MN];
void DP(int x) {
  sz[x] = 1;
  if (ls[x]) {
    DP(ls[x]);
    int w = a[ls[x]] - a[x];
    for (int i = min(m, sz[x]); ~i; --i)
      for (int j = min(m, sz[ls[x]]); ~j; --j)
        dp[x][i + j] =
            max(dp[x][i + j], dp[x][i] + dp[ls[x]][j] + 1ll * w * (m - j) * j);
    sz[x] += sz[ls[x]];
  }
  if (rs[x]) {
    DP(rs[x]);
    int w = a[rs[x]] - a[x];
    for (int i = min(m, sz[x]); ~i; --i)
      for (int j = min(m, sz[rs[x]]); ~j; --j)
        dp[x][i + j] =
            max(dp[x][i + j], dp[x][i] + dp[rs[x]][j] + 1ll * w * (m - j) * j);
    sz[x] += sz[rs[x]];
  }
}
int main() {
  read(n);
  read(m);
  for (int i = (1); i <= (n); ++i) read(a[i]);
  for (int i = 1; i <= n; ++i) {
    while (top && a[stk[top]] > a[i]) top--;
    if (!top)
      ls[i] = stk[1];
    else
      ls[i] = rs[stk[top]], rs[stk[top]] = i;
    stk[++top] = i;
  }
  DP(stk[1]);
  printf("%lld", dp[stk[1]][m]);
  return 0;
}

```