#include <bits/stdc++.h>
using namespace std;
template <typename T>
inline void read(T &f) {
  f = 0;
  T fu = 1;
  char c = getchar();
  while (c < '0' || c > '9') {
    if (c == '-') {
      fu = -1;
    }
    c = getchar();
  }
  while (c >= '0' && c <= '9') {
    f = (f << 3) + (f << 1) + (c & 15);
    c = getchar();
  }
  f *= fu;
}
template <typename T>
void print(T x) {
  if (x < 0) putchar('-'), x = -x;
  if (x < 10)
    putchar(x + 48);
  else
    print(x / 10), putchar(x % 10 + 48);
}
template <typename T>
void print(T x, char t) {
  print(x);
  putchar(t);
}
const int N = 55;
struct edge_t {
  int v, nxt, w;
} G[233333];
queue<int> q;
int a[N][N], id[N][N], d[N], deg[N], f[N], tem[N], dis[N * N], cnt[N * N],
    pre[N * N], vis[N * N], used[N * N], u[N * N], v[N * N], head[N * N];
int n, k, ans = 1e9, tot;
inline void addedge(int u, int v, int w) {
  G[++tot] = (edge_t){v, head[u], w}, head[u] = tot;
}
int find(int x) { return f[x] == x ? x : f[x] = find(f[x]); }
int main() {
  read(n);
  read(k);
  for (int i = 1; i <= k; i++) read(d[i]);
  for (int i = k + 1; i <= n; i++) d[i] = n;
  for (int i = 1; i <= n; i++) {
    for (int j = i + 1; j <= n; j++) read(a[i][j]);
  }
  int m = 0;
  for (int i = 1; i <= n; i++) {
    for (int j = max(k + 1, i + 1); j <= n; j++) {
      id[i][j] = ++m;
      u[m] = i;
      v[m] = j;
    }
  }
  for (int mask = 0; mask < (1 << (k * (k - 1) / 2)); mask++) {
    for (int i = 1; i <= n; i++) f[i] = i;
    memset(deg, 0, sizeof(deg));
    int now = 0, cando = 1, sum = 0;
    for (int u = 1; u <= k; u++) {
      for (int v = u + 1; v <= k; v++) {
        if ((mask >> now) & 1) {
          int x = find(u), y = find(v);
          if (x == y) cando = 0;
          ++deg[u];
          ++deg[v];
          f[x] = y;
          sum += a[u][v];
        }
        ++now;
      }
    }
    for (int i = 1; i <= k; i++) {
      if (deg[i] > d[i]) {
        cando = 0;
      }
    }
    if (!cando) continue;
    memcpy(tem, f, sizeof(tem));
    memset(used, 0, sizeof(used));
    while (1) {
      memset(head, 0, (m + 2) * 4);
      tot = 0;
      int s = 0, t = m + 1;
      for (int i = 1; i <= m; i++) {
        if (used[i]) {
          memcpy(f, tem, sizeof(f));
          for (int j = 1; j <= m; j++) {
            if (used[j] && i != j) {
              f[find(u[j])] = find(v[j]);
            }
          }
          for (int j = 1; j <= m; j++) {
            if (!used[j] && find(u[j]) != find(v[j])) {
              addedge(i, j, a[u[j]][v[j]]);
            }
          }
          --deg[u[i]];
          --deg[v[i]];
          for (int j = 1; j <= m; j++) {
            if (!used[j] && deg[u[j]] < d[u[j]] && deg[v[j]] < d[v[j]]) {
              addedge(j, i, -a[u[i]][v[i]]);
            }
          }
          ++deg[u[i]];
          ++deg[v[i]];
        }
      }
      memcpy(f, tem, sizeof(f));
      for (int i = 1; i <= m; i++) {
        if (used[i]) {
          f[find(u[i])] = find(v[i]);
        }
      }
      for (int i = 1; i <= m; i++) {
        if (!used[i]) {
          if (find(u[i]) != find(v[i])) {
            addedge(s, i, a[u[i]][v[i]]);
          }
          if (deg[u[i]] < d[u[i]] && deg[v[i]] < d[v[i]]) {
            addedge(i, t, 0);
          }
        }
      }
      memset(dis, 0x3f, (m + 2) * 4);
      q.push(s);
      dis[s] = 0;
      vis[s] = 1;
      while (!q.empty()) {
        int u = q.front();
        q.pop();
        vis[u] = 0;
        for (int i = head[u]; i; i = G[i].nxt) {
          int v = G[i].v;
          if (dis[v] > dis[u] + G[i].w ||
              (dis[v] == dis[u] + G[i].w && cnt[v] > cnt[u] + 1)) {
            dis[v] = dis[u] + G[i].w;
            cnt[v] = cnt[u] + 1;
            pre[v] = u;
            if (!vis[v]) {
              vis[v] = 1;
              q.push(v);
            }
          }
        }
      }
      if (dis[t] == 0x3f3f3f3f) break;
      sum += dis[t];
      int tmp = pre[t];
      while (tmp) {
        if (used[tmp])
          --deg[u[tmp]], --deg[v[tmp]];
        else
          ++deg[u[tmp]], ++deg[v[tmp]];
        used[tmp] ^= 1;
        tmp = pre[tmp];
      }
    }
    int ecnt = __builtin_popcount(mask);
    for (int i = 1; i <= m; i++) ecnt += used[i];
    if (ecnt == n - 1) ans = min(ans, sum);
  }
  print(ans, '\n');
  return 0;
}

### Prompt

Construct a CPP code solution to the problem outlined:

<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;
template <typename T>
inline void read(T &f) {
  f = 0;
  T fu = 1;
  char c = getchar();
  while (c < '0' || c > '9') {
    if (c == '-') {
      fu = -1;
    }
    c = getchar();
  }
  while (c >= '0' && c <= '9') {
    f = (f << 3) + (f << 1) + (c & 15);
    c = getchar();
  }
  f *= fu;
}
template <typename T>
void print(T x) {
  if (x < 0) putchar('-'), x = -x;
  if (x < 10)
    putchar(x + 48);
  else
    print(x / 10), putchar(x % 10 + 48);
}
template <typename T>
void print(T x, char t) {
  print(x);
  putchar(t);
}
const int N = 55;
struct edge_t {
  int v, nxt, w;
} G[233333];
queue<int> q;
int a[N][N], id[N][N], d[N], deg[N], f[N], tem[N], dis[N * N], cnt[N * N],
    pre[N * N], vis[N * N], used[N * N], u[N * N], v[N * N], head[N * N];
int n, k, ans = 1e9, tot;
inline void addedge(int u, int v, int w) {
  G[++tot] = (edge_t){v, head[u], w}, head[u] = tot;
}
int find(int x) { return f[x] == x ? x : f[x] = find(f[x]); }
int main() {
  read(n);
  read(k);
  for (int i = 1; i <= k; i++) read(d[i]);
  for (int i = k + 1; i <= n; i++) d[i] = n;
  for (int i = 1; i <= n; i++) {
    for (int j = i + 1; j <= n; j++) read(a[i][j]);
  }
  int m = 0;
  for (int i = 1; i <= n; i++) {
    for (int j = max(k + 1, i + 1); j <= n; j++) {
      id[i][j] = ++m;
      u[m] = i;
      v[m] = j;
    }
  }
  for (int mask = 0; mask < (1 << (k * (k - 1) / 2)); mask++) {
    for (int i = 1; i <= n; i++) f[i] = i;
    memset(deg, 0, sizeof(deg));
    int now = 0, cando = 1, sum = 0;
    for (int u = 1; u <= k; u++) {
      for (int v = u + 1; v <= k; v++) {
        if ((mask >> now) & 1) {
          int x = find(u), y = find(v);
          if (x == y) cando = 0;
          ++deg[u];
          ++deg[v];
          f[x] = y;
          sum += a[u][v];
        }
        ++now;
      }
    }
    for (int i = 1; i <= k; i++) {
      if (deg[i] > d[i]) {
        cando = 0;
      }
    }
    if (!cando) continue;
    memcpy(tem, f, sizeof(tem));
    memset(used, 0, sizeof(used));
    while (1) {
      memset(head, 0, (m + 2) * 4);
      tot = 0;
      int s = 0, t = m + 1;
      for (int i = 1; i <= m; i++) {
        if (used[i]) {
          memcpy(f, tem, sizeof(f));
          for (int j = 1; j <= m; j++) {
            if (used[j] && i != j) {
              f[find(u[j])] = find(v[j]);
            }
          }
          for (int j = 1; j <= m; j++) {
            if (!used[j] && find(u[j]) != find(v[j])) {
              addedge(i, j, a[u[j]][v[j]]);
            }
          }
          --deg[u[i]];
          --deg[v[i]];
          for (int j = 1; j <= m; j++) {
            if (!used[j] && deg[u[j]] < d[u[j]] && deg[v[j]] < d[v[j]]) {
              addedge(j, i, -a[u[i]][v[i]]);
            }
          }
          ++deg[u[i]];
          ++deg[v[i]];
        }
      }
      memcpy(f, tem, sizeof(f));
      for (int i = 1; i <= m; i++) {
        if (used[i]) {
          f[find(u[i])] = find(v[i]);
        }
      }
      for (int i = 1; i <= m; i++) {
        if (!used[i]) {
          if (find(u[i]) != find(v[i])) {
            addedge(s, i, a[u[i]][v[i]]);
          }
          if (deg[u[i]] < d[u[i]] && deg[v[i]] < d[v[i]]) {
            addedge(i, t, 0);
          }
        }
      }
      memset(dis, 0x3f, (m + 2) * 4);
      q.push(s);
      dis[s] = 0;
      vis[s] = 1;
      while (!q.empty()) {
        int u = q.front();
        q.pop();
        vis[u] = 0;
        for (int i = head[u]; i; i = G[i].nxt) {
          int v = G[i].v;
          if (dis[v] > dis[u] + G[i].w ||
              (dis[v] == dis[u] + G[i].w && cnt[v] > cnt[u] + 1)) {
            dis[v] = dis[u] + G[i].w;
            cnt[v] = cnt[u] + 1;
            pre[v] = u;
            if (!vis[v]) {
              vis[v] = 1;
              q.push(v);
            }
          }
        }
      }
      if (dis[t] == 0x3f3f3f3f) break;
      sum += dis[t];
      int tmp = pre[t];
      while (tmp) {
        if (used[tmp])
          --deg[u[tmp]], --deg[v[tmp]];
        else
          ++deg[u[tmp]], ++deg[v[tmp]];
        used[tmp] ^= 1;
        tmp = pre[tmp];
      }
    }
    int ecnt = __builtin_popcount(mask);
    for (int i = 1; i <= m; i++) ecnt += used[i];
    if (ecnt == n - 1) ans = min(ans, sum);
  }
  print(ans, '\n');
  return 0;
}

```