#include <bits/stdc++.h>
using namespace std;
int n, k, d[55], G[55][55];
int bas[55][55], fa[55], las[55], fucked[55][55];
int ans = 1e9;
int GF(int x) { return x == fa[x] ? x : fa[x] = GF(fa[x]); }
namespace nz {
vector<int> G[3030];
int st = 3001, en = 3002, val[3030];
void init() {
  for (int i = 0; i <= en; ++i) G[i].clear();
}
void adde(int x, int y) { G[x].push_back(y); }
int d[3030], in[3030], pre[3030];
int fuck() {
  memset(d, 33, sizeof d);
  memset(in, 0, sizeof in);
  memset(pre, 0, sizeof pre);
  d[st] = 0;
  queue<int> q;
  q.push(st);
  for (int tim = 0; q.size();) {
    int x = q.front();
    q.pop();
    in[x] = 0;
    for (auto y : G[x]) {
      int z = d[x] + val[y];
      if (z < d[y]) {
        d[y] = z;
        pre[y] = x;
        if (!in[y]) q.push(y), in[y] = 1;
      }
    }
  }
  int sum = 0;
  for (int p = en; p; p = pre[p]) {
    if (p != st && p != en) {
      int i = (p - 1) / n, j = (p - 1) % n + 1;
      bas[i][j] ^= 1;
    }
    sum += val[p];
  }
  return d[en];
}
}  // namespace nz
int ID(int i, int j) { return i * n + j; }
int ID(pair<int, int> p) { return ID(p.first, p.second); }
void supermain() {
  for (int i = 1; i <= k; ++i) fa[i] = i, las[i] = d[i];
  int nowsum = 0, aim = n - 1;
  for (int i = 1; i <= k; ++i)
    for (int j = i + 1; j <= k; ++j)
      if (bas[i][j]) {
        nowsum += G[i][j];
        if (GF(i) == GF(j)) return;
        fa[GF(i)] = GF(j);
        --las[i];
        --las[j];
        --aim;
        if (las[i] < 0 || las[j] < 0) return;
      }
  for (; aim--;) {
    nz::init();
    for (int i = 1; i <= n; ++i) fa[i] = i, las[i] = d[i];
    vector<pair<int, int> > vec, vecall;
    for (int i = 1; i <= n; ++i)
      for (int j = i + 1; j <= n; ++j)
        if (bas[i][j]) {
          if (i <= k) --las[i];
          if (j <= k) --las[j];
          fa[GF(i)] = GF(j);
          vecall.push_back({i, j});
          if (j > k) vec.push_back({i, j});
        }
    for (int i = 1; i <= n; ++i)
      for (int j = i + 1; j <= n; ++j)
        nz::val[ID(i, j)] = bas[i][j] ? -G[i][j] : G[i][j];
    memset(fucked, 0, sizeof fucked);
    for (int i = 1; i <= n; ++i)
      for (int j = i + 1; j <= n; ++j) {
        if (j <= k) continue;
        if (bas[i][j]) continue;
        if (GF(i) != GF(j)) nz::adde(nz::st, ID(i, j)), fucked[i][j] = 1;
        if (i > k || las[i] > 0) nz::adde(ID(i, j), nz::en);
      }
    for (auto o : vec) {
      for (int i = 1; i <= n; ++i) fa[i] = i;
      for (auto p : vecall)
        if (p != o) fa[GF(p.first)] = GF(p.second);
      for (int i = 1; i <= n; ++i)
        for (int j = i + 1; j <= n; ++j) {
          if (j <= k) continue;
          if (bas[i][j]) continue;
          if (GF(i) != GF(j) && !fucked[i][j]) nz::adde(ID(o), ID(i, j));
          if (i <= k && las[i] == 0 && i == o.first) nz::adde(ID(i, j), ID(o));
        }
    }
    nowsum += nz::fuck();
    if (nowsum > 1e8) return;
  }
  ans = min(ans, nowsum);
}
int main() {
  cin >> n >> k;
  for (int i = 1; i <= k; ++i) cin >> d[i];
  for (int i = 1; i <= n; ++i) {
    for (int j = i + 1; j <= n; ++j) {
      cin >> G[i][j];
      G[j][i] = G[i][j];
    }
  }
  for (int S = 0; S < (1 << k * (k - 1) / 2); ++S) {
    memset(bas, 0, sizeof bas);
    int cnt = 0;
    for (int i = 1; i <= k; ++i)
      for (int j = i + 1; j <= k; ++j) {
        int c = S >> cnt & 1;
        cnt += 1;
        bas[i][j] = bas[j][i] = c;
      }
    supermain();
  }
  cout << ans << endl;
}

### 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;
int n, k, d[55], G[55][55];
int bas[55][55], fa[55], las[55], fucked[55][55];
int ans = 1e9;
int GF(int x) { return x == fa[x] ? x : fa[x] = GF(fa[x]); }
namespace nz {
vector<int> G[3030];
int st = 3001, en = 3002, val[3030];
void init() {
  for (int i = 0; i <= en; ++i) G[i].clear();
}
void adde(int x, int y) { G[x].push_back(y); }
int d[3030], in[3030], pre[3030];
int fuck() {
  memset(d, 33, sizeof d);
  memset(in, 0, sizeof in);
  memset(pre, 0, sizeof pre);
  d[st] = 0;
  queue<int> q;
  q.push(st);
  for (int tim = 0; q.size();) {
    int x = q.front();
    q.pop();
    in[x] = 0;
    for (auto y : G[x]) {
      int z = d[x] + val[y];
      if (z < d[y]) {
        d[y] = z;
        pre[y] = x;
        if (!in[y]) q.push(y), in[y] = 1;
      }
    }
  }
  int sum = 0;
  for (int p = en; p; p = pre[p]) {
    if (p != st && p != en) {
      int i = (p - 1) / n, j = (p - 1) % n + 1;
      bas[i][j] ^= 1;
    }
    sum += val[p];
  }
  return d[en];
}
}  // namespace nz
int ID(int i, int j) { return i * n + j; }
int ID(pair<int, int> p) { return ID(p.first, p.second); }
void supermain() {
  for (int i = 1; i <= k; ++i) fa[i] = i, las[i] = d[i];
  int nowsum = 0, aim = n - 1;
  for (int i = 1; i <= k; ++i)
    for (int j = i + 1; j <= k; ++j)
      if (bas[i][j]) {
        nowsum += G[i][j];
        if (GF(i) == GF(j)) return;
        fa[GF(i)] = GF(j);
        --las[i];
        --las[j];
        --aim;
        if (las[i] < 0 || las[j] < 0) return;
      }
  for (; aim--;) {
    nz::init();
    for (int i = 1; i <= n; ++i) fa[i] = i, las[i] = d[i];
    vector<pair<int, int> > vec, vecall;
    for (int i = 1; i <= n; ++i)
      for (int j = i + 1; j <= n; ++j)
        if (bas[i][j]) {
          if (i <= k) --las[i];
          if (j <= k) --las[j];
          fa[GF(i)] = GF(j);
          vecall.push_back({i, j});
          if (j > k) vec.push_back({i, j});
        }
    for (int i = 1; i <= n; ++i)
      for (int j = i + 1; j <= n; ++j)
        nz::val[ID(i, j)] = bas[i][j] ? -G[i][j] : G[i][j];
    memset(fucked, 0, sizeof fucked);
    for (int i = 1; i <= n; ++i)
      for (int j = i + 1; j <= n; ++j) {
        if (j <= k) continue;
        if (bas[i][j]) continue;
        if (GF(i) != GF(j)) nz::adde(nz::st, ID(i, j)), fucked[i][j] = 1;
        if (i > k || las[i] > 0) nz::adde(ID(i, j), nz::en);
      }
    for (auto o : vec) {
      for (int i = 1; i <= n; ++i) fa[i] = i;
      for (auto p : vecall)
        if (p != o) fa[GF(p.first)] = GF(p.second);
      for (int i = 1; i <= n; ++i)
        for (int j = i + 1; j <= n; ++j) {
          if (j <= k) continue;
          if (bas[i][j]) continue;
          if (GF(i) != GF(j) && !fucked[i][j]) nz::adde(ID(o), ID(i, j));
          if (i <= k && las[i] == 0 && i == o.first) nz::adde(ID(i, j), ID(o));
        }
    }
    nowsum += nz::fuck();
    if (nowsum > 1e8) return;
  }
  ans = min(ans, nowsum);
}
int main() {
  cin >> n >> k;
  for (int i = 1; i <= k; ++i) cin >> d[i];
  for (int i = 1; i <= n; ++i) {
    for (int j = i + 1; j <= n; ++j) {
      cin >> G[i][j];
      G[j][i] = G[i][j];
    }
  }
  for (int S = 0; S < (1 << k * (k - 1) / 2); ++S) {
    memset(bas, 0, sizeof bas);
    int cnt = 0;
    for (int i = 1; i <= k; ++i)
      for (int j = i + 1; j <= k; ++j) {
        int c = S >> cnt & 1;
        cnt += 1;
        bas[i][j] = bas[j][i] = c;
      }
    supermain();
  }
  cout << ans << endl;
}

```