#include <bits/stdc++.h>
using namespace std;
using LL = long long;
constexpr int maxn = 50;
int w[maxn][maxn];
int p[maxn];
int gp(int u) { return p[u] == u ? u : p[u] = gp(p[u]); }
vector<pair<int, int>> pr[100 + 1];
int n, k, d[maxn], e[maxn];
pair<int, vector<pair<int, int>>> get(vector<pair<int, int>>& cur, int u,
                                      int v) {
  for (int i = 0; i < n; i += 1) p[i] = i;
  vector<pair<int, int>> ncur;
  LL nans = 0;
  for (int i = 0; i < k; i += 1) e[i] = 0;
  for (auto [x, y] : cur) {
    if (w[u][v] < w[x][y]) {
      int pu = gp(u), pv = gp(v);
      if (pu != pv) {
        p[pu] = pv;
        ncur.push_back({u, v});
        nans += w[u][v];
        e[u] += 1;
        e[v] += 1;
      }
    }
    int px = gp(x), py = gp(y);
    if (px != py) {
      p[px] = py;
      ncur.push_back({x, y});
      nans += w[x][y];
      e[x] += 1;
      e[y] += 1;
    }
  }
  for (int i = 0; i < k; i += 1)
    if (e[i] > d[i]) return {INT_MAX, {}};
  return {nans, ncur};
}
int main() {
  cin.tie(nullptr)->sync_with_stdio(false);
  cin >> n >> k;
  for (int i = 0; i < k; i += 1) cin >> d[i];
  for (int i = 0; i < n; i += 1)
    for (int j = i + 1; j < n; j += 1) {
      cin >> w[i][j];
      w[j][i] = w[i][j];
      pr[w[i][j]].push_back({i, j});
    }
  for (int i = k; i < n; i += 1) p[i] = i;
  vector<pair<int, int>> p;
  for (int i = 0; i < n; i += 1)
    for (int j = i + 1; j < n; j += 1) p.push_back({i, j});
  int res = INT_MAX;
  srand(time(0));
  for (int i = 0; i < 500; i += 1) {
    random_shuffle(p.begin(), p.end());
    int ans = 0;
    vector<pair<int, int>> cur;
    int r = rand() % (n - k) + k;
    for (int i = 0; i < n; i += 1)
      if (i != r) {
        cur.push_back({i, r});
        ans += w[i][r];
      }
    sort(cur.begin(), cur.end(),
         [&](const pair<int, int>& p, const pair<int, int>& q) {
           return w[p.first][p.second] < w[q.first][q.second];
         });
    while (true) {
      res = min(res, ans);
      int ok = 1;
      for (auto [i, j] : p) {
        auto [nans, ncur] = get(cur, i, j);
        if (nans < ans) {
          ans = nans;
          ncur.swap(cur);
          ok = 0;
        }
      }
      if (ok) break;
    }
    res = min(res, ans);
  }
  cout << res;
  return 0;
}

### Prompt

Generate a CPP solution to the following problem:

<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

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
using LL = long long;
constexpr int maxn = 50;
int w[maxn][maxn];
int p[maxn];
int gp(int u) { return p[u] == u ? u : p[u] = gp(p[u]); }
vector<pair<int, int>> pr[100 + 1];
int n, k, d[maxn], e[maxn];
pair<int, vector<pair<int, int>>> get(vector<pair<int, int>>& cur, int u,
                                      int v) {
  for (int i = 0; i < n; i += 1) p[i] = i;
  vector<pair<int, int>> ncur;
  LL nans = 0;
  for (int i = 0; i < k; i += 1) e[i] = 0;
  for (auto [x, y] : cur) {
    if (w[u][v] < w[x][y]) {
      int pu = gp(u), pv = gp(v);
      if (pu != pv) {
        p[pu] = pv;
        ncur.push_back({u, v});
        nans += w[u][v];
        e[u] += 1;
        e[v] += 1;
      }
    }
    int px = gp(x), py = gp(y);
    if (px != py) {
      p[px] = py;
      ncur.push_back({x, y});
      nans += w[x][y];
      e[x] += 1;
      e[y] += 1;
    }
  }
  for (int i = 0; i < k; i += 1)
    if (e[i] > d[i]) return {INT_MAX, {}};
  return {nans, ncur};
}
int main() {
  cin.tie(nullptr)->sync_with_stdio(false);
  cin >> n >> k;
  for (int i = 0; i < k; i += 1) cin >> d[i];
  for (int i = 0; i < n; i += 1)
    for (int j = i + 1; j < n; j += 1) {
      cin >> w[i][j];
      w[j][i] = w[i][j];
      pr[w[i][j]].push_back({i, j});
    }
  for (int i = k; i < n; i += 1) p[i] = i;
  vector<pair<int, int>> p;
  for (int i = 0; i < n; i += 1)
    for (int j = i + 1; j < n; j += 1) p.push_back({i, j});
  int res = INT_MAX;
  srand(time(0));
  for (int i = 0; i < 500; i += 1) {
    random_shuffle(p.begin(), p.end());
    int ans = 0;
    vector<pair<int, int>> cur;
    int r = rand() % (n - k) + k;
    for (int i = 0; i < n; i += 1)
      if (i != r) {
        cur.push_back({i, r});
        ans += w[i][r];
      }
    sort(cur.begin(), cur.end(),
         [&](const pair<int, int>& p, const pair<int, int>& q) {
           return w[p.first][p.second] < w[q.first][q.second];
         });
    while (true) {
      res = min(res, ans);
      int ok = 1;
      for (auto [i, j] : p) {
        auto [nans, ncur] = get(cur, i, j);
        if (nans < ans) {
          ans = nans;
          ncur.swap(cur);
          ok = 0;
        }
      }
      if (ok) break;
    }
    res = min(res, ans);
  }
  cout << res;
  return 0;
}

```