#include <bits/stdc++.h>
template <typename T>
bool mincheck(T &a, T b) {
  return (b < a) ? a = b, 1 : 0;
}
template <typename T>
bool chkmax(T &a, T b) {
  return (b > a) ? a = b, 1 : 0;
}
long long ksm(long long a, long long b) {
  if (b == 0) return 1;
  long long ns = ksm(a, b >> 1);
  ns = ns * ns % 998244353;
  if (b & 1) ns = ns * a % 998244353;
  return ns;
}
using namespace std;
const int maxinun = 305;
struct th {
  int u, v;
  int w;
  th() {}
  th(int a, int b, int c) { u = a, v = b, w = c; }
} p[maxinun];
int n, k;
int cnt = 0;
int fa[maxinun];
int gmh(int a) {
  if (fa[a] == a) return a;
  return fa[a] = gmh(fa[a]);
}
void ini() {
  for (int i = 1; i <= n; i++) fa[i] = i;
}
void lk(int a, int b) { fa[gmh(a)] = gmh(b); }
vector<pair<int, int> > eg[maxinun];
int dis[maxinun];
int S, T;
int pre[maxinun];
const int N = 55;
int fl[maxinun];
int d[N], cd[N];
int w[N][N];
vector<pair<int, int> > preg;
int nans = 0;
const int inf = 50000;
void ade(int u, int v, int w) { eg[u].push_back(make_pair(v, w)); }
int q[maxinun * maxinun], fr, ed;
int inq[maxinun];
bool bfs() {
  S = cnt + 1, T = cnt + 2;
  for (int i = 1; i <= T; i++) eg[i].clear();
  vector<int> fls;
  for (int i = 1; i <= cnt; i++) {
    if (fl[i]) fls.push_back(i);
  }
  for (int i = 0; i <= cnt; i++) {
    if (i != 0 && !fl[i]) continue;
    ini();
    for (auto v : preg) lk(v.first, v.second);
    for (auto j : fls) {
      if (j == i) continue;
      lk(p[j].u, p[j].v);
    }
    int nid = i;
    if (i == 0) nid = S;
    for (int i = 1; i <= cnt; i++) {
      if (fl[i]) continue;
      if (gmh(p[i].u) != gmh(p[i].v)) ade(nid, i, inf - p[i].w);
    }
  }
  for (int i = 0; i <= cnt; i++) {
    if (i != 0 && !fl[i]) continue;
    memset(cd, 0, sizeof(cd));
    for (auto v : preg) cd[v.first] += 1, cd[v.second] += 1;
    for (auto j : fls) {
      if (j == i) continue;
      cd[p[j].u] += 1, cd[p[j].v] += 1;
    }
    int nid = i;
    if (i == 0) nid = T;
    int nw = inf - p[nid].w;
    if (nid == T) nw = 0;
    for (int i = 1; i <= cnt; i++) {
      if (fl[i]) continue;
      if (cd[p[i].u] < d[p[i].u] && cd[p[i].v] < d[p[i].v]) ade(i, nid, -nw);
    }
  }
  for (int i = 1; i <= T; i++) dis[i] = -inf, inq[i] = 0;
  int fr = 0, ed = 0;
  dis[S] = 0;
  q[ed++] = S, inq[S] = 1;
  while (fr < ed) {
    int cur = q[fr++];
    inq[cur] = 0;
    for (auto v : eg[cur]) {
      int eid = v.first, ew = v.second;
      if (chkmax(dis[eid], dis[cur] + ew)) {
        pre[eid] = cur;
        if (!inq[eid]) q[ed++] = eid, inq[eid] = 1;
      }
    }
  }
  if (dis[T] <= 0) return 0;
  vector<int> cc;
  int ee = pre[T];
  while (1) {
    cc.push_back(ee);
    ee = pre[ee];
    if (ee == S) break;
  }
  nans += dis[T];
  for (auto v : cc) fl[v] ^= 1;
  return 1;
}
int main() {
  cin >> n >> k;
  for (int i = 1; i <= k; i++) cin >> d[i];
  for (int i = k + 1; i <= n; i++) d[i] = 1e9;
  for (int i = 1; i <= n; i++)
    for (int j = i + 1; j <= n; j++) scanf("%d", &w[i][j]);
  int ans = 1e9;
  ini();
  vector<array<int, 3> > u;
  for (int i = k + 1; i <= n; i++)
    for (int j = i + 1; j <= n; j++) u.push_back({w[i][j], i, j});
  sort(u.begin(), u.end());
  for (auto s : u) {
    if (gmh(s[1]) == gmh(s[2])) continue;
    lk(s[1], s[2]);
    p[++cnt] = th(s[1], s[2], s[0]);
  }
  for (int i = 1; i <= k; i++)
    for (int j = k + 1; j <= n; j++) p[++cnt] = th(i, j, w[i][j]);
  for (int i = 0; i < (1 << (k * (k - 1) / 2)); i++) {
    ini();
    preg.clear();
    memset(cd, 0, sizeof(cd));
    nans = 0;
    int ncnt = 0;
    for (int u = 1; u <= k; u++)
      for (int v = u + 1; v <= k; v++) {
        if (i & (1 << ncnt)) preg.push_back(make_pair(u, v));
        ncnt += 1;
      }
    int flag = 1;
    for (auto s : preg) {
      if (gmh(s.first) == gmh(s.second)) flag = 0;
      lk(s.first, s.second);
      nans += inf - w[s.first][s.second];
      cd[s.first] += 1, cd[s.second] += 1;
    }
    for (int i = 1; i <= k; i++)
      if (cd[i] > d[i]) flag = 0;
    if (!flag) continue;
    memset(fl, 0, sizeof(fl));
    for (int m = 0; m < n - 1 - preg.size(); m++) {
      flag &= bfs();
      if (!flag) break;
    }
    if (flag) {
      mincheck(ans, (n - 1) * inf - nans);
    }
  }
  cout << ans << endl;
  return (0 - 0);
}

### Prompt

Please formulate 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>
template <typename T>
bool mincheck(T &a, T b) {
  return (b < a) ? a = b, 1 : 0;
}
template <typename T>
bool chkmax(T &a, T b) {
  return (b > a) ? a = b, 1 : 0;
}
long long ksm(long long a, long long b) {
  if (b == 0) return 1;
  long long ns = ksm(a, b >> 1);
  ns = ns * ns % 998244353;
  if (b & 1) ns = ns * a % 998244353;
  return ns;
}
using namespace std;
const int maxinun = 305;
struct th {
  int u, v;
  int w;
  th() {}
  th(int a, int b, int c) { u = a, v = b, w = c; }
} p[maxinun];
int n, k;
int cnt = 0;
int fa[maxinun];
int gmh(int a) {
  if (fa[a] == a) return a;
  return fa[a] = gmh(fa[a]);
}
void ini() {
  for (int i = 1; i <= n; i++) fa[i] = i;
}
void lk(int a, int b) { fa[gmh(a)] = gmh(b); }
vector<pair<int, int> > eg[maxinun];
int dis[maxinun];
int S, T;
int pre[maxinun];
const int N = 55;
int fl[maxinun];
int d[N], cd[N];
int w[N][N];
vector<pair<int, int> > preg;
int nans = 0;
const int inf = 50000;
void ade(int u, int v, int w) { eg[u].push_back(make_pair(v, w)); }
int q[maxinun * maxinun], fr, ed;
int inq[maxinun];
bool bfs() {
  S = cnt + 1, T = cnt + 2;
  for (int i = 1; i <= T; i++) eg[i].clear();
  vector<int> fls;
  for (int i = 1; i <= cnt; i++) {
    if (fl[i]) fls.push_back(i);
  }
  for (int i = 0; i <= cnt; i++) {
    if (i != 0 && !fl[i]) continue;
    ini();
    for (auto v : preg) lk(v.first, v.second);
    for (auto j : fls) {
      if (j == i) continue;
      lk(p[j].u, p[j].v);
    }
    int nid = i;
    if (i == 0) nid = S;
    for (int i = 1; i <= cnt; i++) {
      if (fl[i]) continue;
      if (gmh(p[i].u) != gmh(p[i].v)) ade(nid, i, inf - p[i].w);
    }
  }
  for (int i = 0; i <= cnt; i++) {
    if (i != 0 && !fl[i]) continue;
    memset(cd, 0, sizeof(cd));
    for (auto v : preg) cd[v.first] += 1, cd[v.second] += 1;
    for (auto j : fls) {
      if (j == i) continue;
      cd[p[j].u] += 1, cd[p[j].v] += 1;
    }
    int nid = i;
    if (i == 0) nid = T;
    int nw = inf - p[nid].w;
    if (nid == T) nw = 0;
    for (int i = 1; i <= cnt; i++) {
      if (fl[i]) continue;
      if (cd[p[i].u] < d[p[i].u] && cd[p[i].v] < d[p[i].v]) ade(i, nid, -nw);
    }
  }
  for (int i = 1; i <= T; i++) dis[i] = -inf, inq[i] = 0;
  int fr = 0, ed = 0;
  dis[S] = 0;
  q[ed++] = S, inq[S] = 1;
  while (fr < ed) {
    int cur = q[fr++];
    inq[cur] = 0;
    for (auto v : eg[cur]) {
      int eid = v.first, ew = v.second;
      if (chkmax(dis[eid], dis[cur] + ew)) {
        pre[eid] = cur;
        if (!inq[eid]) q[ed++] = eid, inq[eid] = 1;
      }
    }
  }
  if (dis[T] <= 0) return 0;
  vector<int> cc;
  int ee = pre[T];
  while (1) {
    cc.push_back(ee);
    ee = pre[ee];
    if (ee == S) break;
  }
  nans += dis[T];
  for (auto v : cc) fl[v] ^= 1;
  return 1;
}
int main() {
  cin >> n >> k;
  for (int i = 1; i <= k; i++) cin >> d[i];
  for (int i = k + 1; i <= n; i++) d[i] = 1e9;
  for (int i = 1; i <= n; i++)
    for (int j = i + 1; j <= n; j++) scanf("%d", &w[i][j]);
  int ans = 1e9;
  ini();
  vector<array<int, 3> > u;
  for (int i = k + 1; i <= n; i++)
    for (int j = i + 1; j <= n; j++) u.push_back({w[i][j], i, j});
  sort(u.begin(), u.end());
  for (auto s : u) {
    if (gmh(s[1]) == gmh(s[2])) continue;
    lk(s[1], s[2]);
    p[++cnt] = th(s[1], s[2], s[0]);
  }
  for (int i = 1; i <= k; i++)
    for (int j = k + 1; j <= n; j++) p[++cnt] = th(i, j, w[i][j]);
  for (int i = 0; i < (1 << (k * (k - 1) / 2)); i++) {
    ini();
    preg.clear();
    memset(cd, 0, sizeof(cd));
    nans = 0;
    int ncnt = 0;
    for (int u = 1; u <= k; u++)
      for (int v = u + 1; v <= k; v++) {
        if (i & (1 << ncnt)) preg.push_back(make_pair(u, v));
        ncnt += 1;
      }
    int flag = 1;
    for (auto s : preg) {
      if (gmh(s.first) == gmh(s.second)) flag = 0;
      lk(s.first, s.second);
      nans += inf - w[s.first][s.second];
      cd[s.first] += 1, cd[s.second] += 1;
    }
    for (int i = 1; i <= k; i++)
      if (cd[i] > d[i]) flag = 0;
    if (!flag) continue;
    memset(fl, 0, sizeof(fl));
    for (int m = 0; m < n - 1 - preg.size(); m++) {
      flag &= bfs();
      if (!flag) break;
    }
    if (flag) {
      mincheck(ans, (n - 1) * inf - nans);
    }
  }
  cout << ans << endl;
  return (0 - 0);
}

```