#include <bits/stdc++.h>
using namespace std;
int read() {
  int ret = 0;
  char c = getchar();
  while (c > '9' || c < '0') c = getchar();
  while (c >= '0' && c <= '9')
    ret = (ret << 3) + (ret << 1) + (c ^ 48), c = getchar();
  return ret;
}
const int maxn = 55;
const int maxk = 6;
const int maxm = 2500;
const int inf = 1e9;
int n, k;
int dlim[maxk];
struct edge {
  int from, to, val;
} e1[15], e2[maxm];
int cnt1, cnt2;
int ans;
int d[maxk];
bool ini[maxm], x[maxm], y[maxm];
int dis[maxm], pre[maxm];
struct dsu {
  int fa[maxn];
  void prework() {
    for (int i = 1; i <= n; i++) fa[i] = i;
  }
  int get(int x) { return x == fa[x] ? x : fa[x] = get(fa[x]); }
  void merge(int x, int y) { fa[get(x)] = get(y); }
  bool check(int x, int y) { return get(x) == get(y); }
} S;
queue<int> q;
bool inq[maxm];
int ret = 0;
bool deb = 0;
struct graph {
  int head[maxm], ver[maxm * maxm], nxt[maxm * maxm], val[maxm * maxm], tot;
  void add(int x, int y, int z) {
    ver[++tot] = y;
    val[tot] = z;
    nxt[tot] = head[x];
    head[x] = tot;
  }
  void clear() {
    tot = 0;
    for (int i = 1; i <= cnt2 + 2; i++) head[i] = 0;
  }
  int dis[maxm], pre[maxm], len[maxm];
  bool inq[maxm];
  void spfa() {
    for (int i = 1; i <= cnt2 + 2; i++)
      dis[i] = 0x3f3f3f3f, inq[i] = 0, pre[i] = 0;
    dis[cnt2 + 1] = 0;
    q.push(cnt2 + 1);
    inq[cnt2 + 1] = 1;
    while (!q.empty()) {
      int now = q.front();
      q.pop();
      inq[now] = 0;
      for (int i = head[now]; i; i = nxt[i])
        if (dis[ver[i]] > dis[now] + val[i] ||
            (dis[ver[i]] == dis[now] + val[i] && len[ver[i]] > len[now] + 1)) {
          dis[ver[i]] = dis[now] + val[i];
          len[ver[i]] = len[now] + 1;
          pre[ver[i]] = now;
          if (!inq[ver[i]]) q.push(ver[i]);
          inq[ver[i]] = 1;
        }
    }
  }
  void update() {
    int now = cnt2 + 2;
    while (now) {
      ini[now] ^= 1;
      if (ini[now])
        ret -= e2[now].val;
      else
        ret += e2[now].val;
      now = pre[now];
    }
  }
} o;
bool calc(int chose) {
  for (int i = 1; i <= k; i++) d[i] = 0;
  S.prework();
  for (int i = 1; i <= cnt1; i++)
    if ((chose >> (i - 1)) & 1) {
      d[e1[i].from]++, d[e1[i].to]++;
      S.merge(e1[i].from, e1[i].to);
    }
  for (int i = 1; i <= cnt2; i++)
    if (ini[i]) {
      if (e2[i].from <= k) d[e2[i].from]++;
      S.merge(e2[i].from, e2[i].to);
    }
  int s = cnt2 + 1, t = cnt2 + 2;
  o.clear();
  for (int i = 1; i <= cnt2; i++) {
    if (ini[i])
      x[i] = y[i] = 0;
    else {
      x[i] = (!S.check(e2[i].from, e2[i].to));
      y[i] = (e2[i].from > k || d[e2[i].from] + 1 <= dlim[e2[i].from]);
      if (x[i]) o.add(s, i, e2[i].val);
      if (y[i]) o.add(i, t, 0);
    }
  }
  for (int i = 1; i <= cnt2; i++) {
    if (!ini[i]) continue;
    S.prework();
    for (int j = 1; j <= cnt2; j++)
      if (ini[j] && j != i) S.merge(e2[j].from, e2[j].to);
    for (int i = 1; i <= cnt1; i++)
      if ((chose >> (i - 1)) & 1) S.merge(e1[i].from, e1[i].to);
    for (int j = 1; j <= cnt2; j++) {
      if (ini[j]) continue;
      if (!S.check(e2[j].from, e2[j].to)) o.add(i, j, e2[j].val);
      if (e2[j].from > k ||
          d[e2[j].from] - (e2[j].from == e2[i].from) < dlim[e2[j].from])
        o.add(j, i, -e2[i].val);
    }
  }
  o.spfa();
  if (o.dis[t] == 0x3f3f3f3f) return false;
  o.update();
  return true;
}
void solve(int chose) {
  for (int i = 1; i <= k; i++) d[i] = 0;
  S.prework();
  ret = 0;
  for (int i = 1; i <= cnt1; i++)
    if ((chose >> (i - 1)) & 1) {
      d[e1[i].from]++;
      d[e1[i].to]++;
      ret += e1[i].val;
      if (d[e1[i].from] > dlim[e1[i].from]) return;
      if (d[e1[i].to] > dlim[e1[i].to]) return;
      if (S.check(e1[i].from, e1[i].to)) return;
      S.merge(e1[i].from, e1[i].to);
    }
  for (int i = 1; i <= cnt2; i++) ini[i] = 0;
  int cnt = 0;
  if (ret > ans) return;
  while (calc(chose)) {
    if (ret > ans) return;
  }
  ret = 0;
  bool flag = 1;
  S.prework();
  for (int i = 1; i <= cnt1; i++)
    if ((chose >> (i - 1)) & 1) S.merge(e1[i].from, e1[i].to), ret += e1[i].val;
  for (int i = 1; i <= cnt2; i++)
    if (ini[i]) S.merge(e2[i].from, e2[i].to), ret += e2[i].val;
  for (int i = 1; i <= n; i++)
    if (!S.check(1, i)) return;
  ans = min(ret, ans);
}
int main() {
  n = read();
  k = read();
  for (int i = 1; i <= k; i++) dlim[i] = read();
  for (int i = 1; i <= n - 1; i++)
    for (int j = 1; j <= n - i; j++)
      if (i <= k && i + j <= k) {
        cnt1++;
        e1[cnt1].from = i;
        e1[cnt1].to = i + j;
        e1[cnt1].val = read();
      } else {
        cnt2++;
        e2[cnt2].from = i;
        e2[cnt2].to = i + j;
        e2[cnt2].val = read();
      }
  ans = inf;
  for (int i = 0; i < (1 << cnt1); i++) solve(i);
  printf("%d\n", ans);
  return 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>
using namespace std;
int read() {
  int ret = 0;
  char c = getchar();
  while (c > '9' || c < '0') c = getchar();
  while (c >= '0' && c <= '9')
    ret = (ret << 3) + (ret << 1) + (c ^ 48), c = getchar();
  return ret;
}
const int maxn = 55;
const int maxk = 6;
const int maxm = 2500;
const int inf = 1e9;
int n, k;
int dlim[maxk];
struct edge {
  int from, to, val;
} e1[15], e2[maxm];
int cnt1, cnt2;
int ans;
int d[maxk];
bool ini[maxm], x[maxm], y[maxm];
int dis[maxm], pre[maxm];
struct dsu {
  int fa[maxn];
  void prework() {
    for (int i = 1; i <= n; i++) fa[i] = i;
  }
  int get(int x) { return x == fa[x] ? x : fa[x] = get(fa[x]); }
  void merge(int x, int y) { fa[get(x)] = get(y); }
  bool check(int x, int y) { return get(x) == get(y); }
} S;
queue<int> q;
bool inq[maxm];
int ret = 0;
bool deb = 0;
struct graph {
  int head[maxm], ver[maxm * maxm], nxt[maxm * maxm], val[maxm * maxm], tot;
  void add(int x, int y, int z) {
    ver[++tot] = y;
    val[tot] = z;
    nxt[tot] = head[x];
    head[x] = tot;
  }
  void clear() {
    tot = 0;
    for (int i = 1; i <= cnt2 + 2; i++) head[i] = 0;
  }
  int dis[maxm], pre[maxm], len[maxm];
  bool inq[maxm];
  void spfa() {
    for (int i = 1; i <= cnt2 + 2; i++)
      dis[i] = 0x3f3f3f3f, inq[i] = 0, pre[i] = 0;
    dis[cnt2 + 1] = 0;
    q.push(cnt2 + 1);
    inq[cnt2 + 1] = 1;
    while (!q.empty()) {
      int now = q.front();
      q.pop();
      inq[now] = 0;
      for (int i = head[now]; i; i = nxt[i])
        if (dis[ver[i]] > dis[now] + val[i] ||
            (dis[ver[i]] == dis[now] + val[i] && len[ver[i]] > len[now] + 1)) {
          dis[ver[i]] = dis[now] + val[i];
          len[ver[i]] = len[now] + 1;
          pre[ver[i]] = now;
          if (!inq[ver[i]]) q.push(ver[i]);
          inq[ver[i]] = 1;
        }
    }
  }
  void update() {
    int now = cnt2 + 2;
    while (now) {
      ini[now] ^= 1;
      if (ini[now])
        ret -= e2[now].val;
      else
        ret += e2[now].val;
      now = pre[now];
    }
  }
} o;
bool calc(int chose) {
  for (int i = 1; i <= k; i++) d[i] = 0;
  S.prework();
  for (int i = 1; i <= cnt1; i++)
    if ((chose >> (i - 1)) & 1) {
      d[e1[i].from]++, d[e1[i].to]++;
      S.merge(e1[i].from, e1[i].to);
    }
  for (int i = 1; i <= cnt2; i++)
    if (ini[i]) {
      if (e2[i].from <= k) d[e2[i].from]++;
      S.merge(e2[i].from, e2[i].to);
    }
  int s = cnt2 + 1, t = cnt2 + 2;
  o.clear();
  for (int i = 1; i <= cnt2; i++) {
    if (ini[i])
      x[i] = y[i] = 0;
    else {
      x[i] = (!S.check(e2[i].from, e2[i].to));
      y[i] = (e2[i].from > k || d[e2[i].from] + 1 <= dlim[e2[i].from]);
      if (x[i]) o.add(s, i, e2[i].val);
      if (y[i]) o.add(i, t, 0);
    }
  }
  for (int i = 1; i <= cnt2; i++) {
    if (!ini[i]) continue;
    S.prework();
    for (int j = 1; j <= cnt2; j++)
      if (ini[j] && j != i) S.merge(e2[j].from, e2[j].to);
    for (int i = 1; i <= cnt1; i++)
      if ((chose >> (i - 1)) & 1) S.merge(e1[i].from, e1[i].to);
    for (int j = 1; j <= cnt2; j++) {
      if (ini[j]) continue;
      if (!S.check(e2[j].from, e2[j].to)) o.add(i, j, e2[j].val);
      if (e2[j].from > k ||
          d[e2[j].from] - (e2[j].from == e2[i].from) < dlim[e2[j].from])
        o.add(j, i, -e2[i].val);
    }
  }
  o.spfa();
  if (o.dis[t] == 0x3f3f3f3f) return false;
  o.update();
  return true;
}
void solve(int chose) {
  for (int i = 1; i <= k; i++) d[i] = 0;
  S.prework();
  ret = 0;
  for (int i = 1; i <= cnt1; i++)
    if ((chose >> (i - 1)) & 1) {
      d[e1[i].from]++;
      d[e1[i].to]++;
      ret += e1[i].val;
      if (d[e1[i].from] > dlim[e1[i].from]) return;
      if (d[e1[i].to] > dlim[e1[i].to]) return;
      if (S.check(e1[i].from, e1[i].to)) return;
      S.merge(e1[i].from, e1[i].to);
    }
  for (int i = 1; i <= cnt2; i++) ini[i] = 0;
  int cnt = 0;
  if (ret > ans) return;
  while (calc(chose)) {
    if (ret > ans) return;
  }
  ret = 0;
  bool flag = 1;
  S.prework();
  for (int i = 1; i <= cnt1; i++)
    if ((chose >> (i - 1)) & 1) S.merge(e1[i].from, e1[i].to), ret += e1[i].val;
  for (int i = 1; i <= cnt2; i++)
    if (ini[i]) S.merge(e2[i].from, e2[i].to), ret += e2[i].val;
  for (int i = 1; i <= n; i++)
    if (!S.check(1, i)) return;
  ans = min(ret, ans);
}
int main() {
  n = read();
  k = read();
  for (int i = 1; i <= k; i++) dlim[i] = read();
  for (int i = 1; i <= n - 1; i++)
    for (int j = 1; j <= n - i; j++)
      if (i <= k && i + j <= k) {
        cnt1++;
        e1[cnt1].from = i;
        e1[cnt1].to = i + j;
        e1[cnt1].val = read();
      } else {
        cnt2++;
        e2[cnt2].from = i;
        e2[cnt2].to = i + j;
        e2[cnt2].val = read();
      }
  ans = inf;
  for (int i = 0; i < (1 << cnt1); i++) solve(i);
  printf("%d\n", ans);
  return 0;
}

```