description: 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].
solution: #include <bits/stdc++.h>
  void sc(int &x) { scanf("%d", &x); }
  void sc(int &x, int &y) { scanf("%d%d", &x, &y); }
  void sc(int &x, int &y, int &z) { scanf("%d%d%d", &x, &y, &z); }
  void sc(long long &x) { scanf("%lld", &x); }
  void sc(long long &x, long long &y) { scanf("%lld%lld", &x, &y); }
  void sc(long long &x, long long &y, long long &z) {
    scanf("%lld%lld%lld", &x, &y, &z);
  }
  void sc(char *x) { scanf("%s", x); }
  void sc(char *x, char *y) { scanf("%s%s", x, y); }
  void sc(char *x, char *y, char *z) { scanf("%s%s%s", x, y, z); }
  void out(int x) { printf("%d\n", x); }
  void out(long long x) { printf("%lld\n", x); }
  void out(int x, int y) { printf("%d %d\n", x, y); }
  void out(long long x, long long y) { printf("%lld %lld\n", x, y); }
  void out(int x, int y, int z) { printf("%d %d %d\n", x, y, z); }
  void out(long long x, long long y, long long z) {
    printf("%lld %lld %lld\n", x, y, z);
  }
  void ast(long long x, long long l, long long r) { assert(x >= l && x <= r); }
  using namespace std;
  const int N = 4005;
  int n, m, top, s[N], si[N], a[N], t[N][2];
  long long dp[N][N], g[N];
  void update(long long &x, long long y) {
    if (y > x) x = y;
  }
  void dfs(int u) {
    dp[u][0] = dp[u][1] = 0;
    si[u] = 1;
    int v = t[u][0];
    if (v) {
      dfs(v);
      memset(g, 0, sizeof(g));
      for (int i = 0; i <= si[u]; i++)
        for (int j = 0; j <= si[v] && i + j <= m; j++)
          update(g[i + j],
                 dp[u][i] + dp[v][j] + 1ll * j * (m - j) * (a[v] - a[u]));
      memcpy(dp[u], g, sizeof(g));
      si[u] += si[v];
    }
    v = t[u][1];
    if (v) {
      dfs(v);
      memset(g, 0, sizeof(g));
      for (int i = 0; i <= si[u]; i++)
        for (int j = 0; j <= si[v] && i + j <= m; j++)
          update(g[i + j],
                 dp[u][i] + dp[v][j] + 1ll * j * (m - j) * (a[v] - a[u]));
      memcpy(dp[u], g, sizeof(g));
      si[u] += si[v];
    }
  }
  void sol(int cas) {
    sc(n, m);
    for (int i = 1; i <= n; i++) sc(a[i]);
    for (int i = 1; i <= n; i++) {
      while (top && a[s[top]] > a[i]) {
        if (a[s[top - 1]] > a[i])
          t[s[top - 1]][1] = s[top];
        else
          t[i][0] = s[top];
        top--;
      }
      s[++top] = i;
    }
    while (top > 1) t[s[top - 1]][1] = s[top], top--;
    dfs(s[top]);
    printf("%lld\n", dp[s[top]][m]);
  }
  int main() {
    srand(time(0));
    int t = 1, cas = 0;
    while (t--) {
      sol(++cas);
    }
  }
  