#if __INCLUDE_LEVEL__ == 0

#include __BASE_FILE__

void Solve() {
  int n, K;
  IN(n, K);
  vector<int64_t> a(K), b(K);
  IN(a, b);
  vector<vector<int>> x(K);
  vector<vector<int64_t>> w(K);
  for (int k : Rep(0, K)) {
    int P;
    IN(P);
    --P;
    x[k].resize(P + 1);
    w[k].resize(P);
    for (int p : Rep1(0, P)) {
      IN(x[k][p]);
      --x[k][p];
      if (p < P) {
        IN(w[k][p]);
      }
    }
  }

  vector<vector<int64_t>> d(K);
  for (int k : Rep(0, K)) {
    d[k].assign(Sz(x[k]), INF64);
  }
  auto d2 = d;
  priority_queue q(greater{}, vector<tuple<int64_t, int, int, int>>{});
  for (int k : Rep(0, K)) {
    for (int p : Rep(0, Sz(x[k]))) {
      if (x[k][p] == 0) {
        q.emplace(d[k][p] = 0, k, p, -1);
      }
    }
  }

  vector<vector<pair<int, int>>> lst(n);
  for (int k : Rep(0, K)) {
    for (int p : Rep(0, Sz(x[k]))) {
      lst[x[k][p]].emplace_back(k, p);
    }
  }
  for (int i : Rep(0, n)) {
    ranges::sort(lst[i], {}, LAMBDA(x, a[x.first]));
  }
  vector<int> lst_ptr(n);

  vector<vector<pair<int64_t, int64_t>>> lines(n);
  vector<int> lines_ptr(n);

  auto Eval = [&](int i) -> int64_t {
    if (lst_ptr[i] == Sz(lst[i])) {
      return INF64;
    }
    auto [k, p] = lst[i][lst_ptr[i]];
    auto Go = [&](int ptr) -> int64_t {
      auto [slope, intercept] = lines[i][ptr];
      return slope * a[k] + intercept;
    };
    while (lines_ptr[i] + 1 < Sz(lines[i]) && Go(lines_ptr[i] + 1) < Go(lines_ptr[i])) {
      ++lines_ptr[i];
    }
    if (lines_ptr[i] == Sz(lines[i])) {
      return INF64;
    }
    return Go(lines_ptr[i]);
  };

  while (Sz(q)) {
    auto [dkp, k, p, t] = q.top();
    q.pop();
    if (dkp != d[k][p]) {
      continue;
    }

    if (p + 1 < Sz(x[k])) {
      if (SetMin(d[k][p + 1], dkp + w[k][p])) {
        q.emplace(d[k][p + 1], k, p + 1, -1);
      }
    }

    if (t != -1) {
      if (++lst_ptr[t] < Sz(lst[t])) {
        if (Eval(t) < INF64) {
          auto [nk, np] = lst[t][lst_ptr[t]];
          if (SetMin(d[nk][np], Eval(t)) || SetMin(d2[nk][np], Eval(t))) {
            q.emplace(d[nk][np], nk, np, t);
          }
        }
      }
    }

    int i = x[k][p];
    if (lines[i].empty() || lines[i].back().first > b[k]) {
      lines[i].emplace_back(b[k], dkp);
      if (Eval(i) < INF64) {
        auto [nk, np] = lst[i][lst_ptr[i]];
        if (SetMin(d[nk][np], Eval(i)) || SetMin(d2[nk][np], Eval(i))) {
          q.emplace(d[nk][np], nk, np, i);
        }
      }
    }
  }

  vector<int64_t> ans(n, INF64);
  for (int k : Rep(0, K)) {
    for (int p : Rep(0, Sz(x[k]))) {
      SetMin(ans[x[k][p]], d[k][p]);
    }
  }
  OUT(ans | views::drop(1));
}

int main() {
  ios::sync_with_stdio(false);
  cin.tie(nullptr);

  Solve();
}

#elif __INCLUDE_LEVEL__ == 1

#include <bits/stdc++.h>

template <class T> concept Range = std::ranges::range<T> && !std::convertible_to<T, std::string_view>;
template <class T> concept Tuple = std::__is_tuple_like<T>::value && !Range<T>;

namespace std {

istream& operator>>(istream& is, Range auto&& r) {
  for (auto&& e : r) is >> e;
  return is;
}
istream& operator>>(istream& is, Tuple auto&& t) {
  apply([&](auto&... xs) { (is >> ... >> xs); }, t);
  return is;
}

ostream& operator<<(ostream& os, Range auto&& r) {
  auto sep = "";
  for (auto&& e : r) os << exchange(sep, " ") << e;
  return os;
}
ostream& operator<<(ostream& os, Tuple auto&& t) {
  auto sep = "";
  apply([&](auto&... xs) { ((os << exchange(sep, " ") << xs), ...); }, t);
  return os;
}

}  // namespace std

using namespace std;

#define LAMBDA(x, ...) ([&](auto&& x) -> decltype(auto) { return __VA_ARGS__; })
#define LAMBDA2(x, y, ...) ([&](auto&& x, auto&& y) -> decltype(auto) { return __VA_ARGS__; })
#define Rep(...) [](int l, int r) { return views::iota(min(l, r), r); }(__VA_ARGS__)
#define Rep1(...) [](int l, int r) { return Rep(l, r + 1); }(__VA_ARGS__)
#define Sz(r) int(size(r))
#define SetMin(...) LAMBDA2(x, y, y < x && (x = y, 1))(__VA_ARGS__)
#define INF64 (INT64_MAX / 2)
#define IN(...) (cin >> forward_as_tuple(__VA_ARGS__))
#define OUT(...) (cout << forward_as_tuple(__VA_ARGS__) << '\n')

#endif  // __INCLUDE_LEVEL__ == 1