description: <image>
  
  William really likes puzzle kits. For one of his birthdays, his friends gifted him a complete undirected edge-weighted graph consisting of n vertices.
  
  He wants to build a spanning tree of this graph, such that for the first k vertices the following condition is satisfied: the degree of a vertex with index i does not exceed d_i. Vertices from k + 1 to n may have any degree.
  
  William wants you to find the minimum weight of a spanning tree that satisfies all the conditions.
  
  A spanning tree is a subset of edges of a graph that forms a tree on all n vertices of the graph. The weight of a spanning tree is defined as the sum of weights of all the edges included in a spanning tree.
  
  Input
  
  The first line of input contains two integers n, k (2 ≤ n ≤ 50, 1 ≤ k ≤ min(n - 1, 5)).
  
  The second line contains k integers d_1, d_2, …, d_k (1 ≤ d_i ≤ n). 
  
  The i-th of the next n - 1 lines contains n - i integers w_{i,i+1}, w_{i,i+2}, …, w_{i,n} (1 ≤ w_{i,j} ≤ 100): weights of edges (i,i+1),(i,i+2),…,(i,n).
  
  Output
  
  Print one integer: the minimum weight of a spanning tree under given degree constraints for the first k vertices. 
  
  Example
  
  Input
  
  
  10 5
  5 3 4 2 1
  29 49 33 12 55 15 32 62 37
  61 26 15 58 15 22 8 58
  37 16 9 39 20 14 58
  10 15 40 3 19 55
  53 13 37 44 52
  23 59 58 4
  69 80 29
  89 28
  48
  
  
  Output
  
  
  95
solution: #include <bits/stdc++.h>
  using namespace std;
  const int N = 53, mod = 1e9 + 7;
  int n, k;
  int d[N], a[N][N];
  vector<pair<int, int> > tmp[105];
  set<pair<int, int> > edge;
  int siz[N];
  vector<int> g[N];
  int f[N];
  int fa(int x) { return f[x] == x ? x : f[x] = fa(f[x]); }
  int dif;
  pair<int, int> del, ad;
  int f2[N];
  void dfs(int x, int fat) {
    f2[x] = fat;
    for (int v : g[x])
      if (v != fat) {
        dfs(v, x);
      }
  }
  int main() {
    scanf("%d%d", &n, &k);
    for (int i = 1; i <= k; ++i) scanf("%d", d + i);
    for (int i = 1; i <= n; ++i)
      for (int j = i + 1; j <= n; ++j) scanf("%d", a[i] + j), a[j][i] = a[i][j];
    for (int i = k + 1; i <= n; ++i)
      for (int j = i + 1; j <= n; ++j) tmp[a[i][j]].push_back(make_pair(i, j));
    for (int i = 1; i <= n; ++i) f[i] = i;
    int ans = 0;
    for (int i = 1; i <= 100; ++i)
      for (auto& p : tmp[i]) {
        int x = fa(p.first), y = fa(p.second);
        if (x != y) f[x] = y, ans += i, edge.insert(p);
      }
    for (int i = 1; i <= k; ++i) {
      int mi = k + 1;
      for (int j = k + 1; j <= n; ++j)
        if (a[i][j] < a[i][mi]) mi = j;
      ans += a[i][mi], edge.insert(make_pair(min(i, mi), max(i, mi)));
    }
    a[0][0] = -mod;
    for (;;) {
      for (int i = 1; i <= n; ++i) g[i].clear();
      for (auto& p : edge)
        g[p.first].push_back(p.second), g[p.second].push_back(p.first);
      for (int i = 1; i <= n; ++i) siz[i] = g[i].size();
      dif = mod;
      for (int i = 1; i <= n; ++i) {
        dfs(i, 0);
        for (int j = 1; j <= n; ++j) {
          int kk = j;
          while (kk != i) {
            bool flag = 0;
            --siz[kk];
            --siz[f2[kk]];
            ++siz[i];
            ++siz[j];
            for (int p = 1; p <= k; ++p)
              if (siz[p] > d[p]) {
                flag = 1;
                break;
              }
            ++siz[kk];
            ++siz[f2[kk]];
            --siz[i];
            --siz[j];
            if (!flag && dif > a[i][j] - a[kk][f2[kk]]) {
              dif = a[i][j] - a[kk][f2[kk]];
              del = make_pair(min(kk, f2[kk]), max(kk, f2[kk]));
              ad = make_pair(min(i, j), max(i, j));
            }
            kk = f2[kk];
          }
        }
      }
      if (dif < 0) {
        ans += dif;
        edge.erase(del);
        edge.insert(ad);
      } else
        break;
    }
    printf("%d\n", ans);
    return 0;
  }
  