#include <bits/stdc++.h>
using namespace std;

using ll = long long;
#define int ll

const int maxn = 4e5 + 10;
struct dt {
    ll k, b;
    dt(ll ak = 0, ll ab = 0) : k(ak), b(ab) {}
    ll get(ll x) {
        return 1ll * k * x + b;
    }
} tr[maxn * 50];
int ls[maxn * 50];
int rs[maxn * 50];
int cnt;
int root[maxn];
void ins(int& i, int l, int r, dt nt) {
    if (i == 0) {
        i = ++cnt;
        tr[i] = nt;
        return;
    }
    if (tr[i].get(l) >= nt.get(l) && tr[i].get(r) >= nt.get(r)) {
        tr[i] = nt;
        return;
    }
    if (tr[i].get(l) <= nt.get(l) && tr[i].get(r) <= nt.get(r)) {
        return;
    }
    int mid = l + r >> 1;
    if (tr[i].get(l) > nt.get(l) || tr[i].get(mid) > nt.get(mid)) {
        ins(ls[i], l, mid, nt);
    }
    if (tr[i].get(mid + 1) > nt.get(mid + 1) || tr[i].get(r) > nt.get(r)) {
        ins(rs[i], mid + 1, r, nt);
    }
    return;
}

ll ask(int i, int l, int r, int x) {
    if (i == 0) return 1e18;
    ll ans = tr[i].get(x);
    if (l == r) return ans;
    int mid = l + r >> 1;
    if (x <= mid)
        ans = min(ans, ask(ls[i], l, mid, x));
    else
        ans = min(ans, ask(rs[i], mid + 1, r, x));
    return ans;
}
void modify(int rt, int k, int b) {
    // insert kx + b into rt
    ins(root[rt], 1, 1e6, dt(k, b));
}
ll query(int rt, int x) {
    // get f(x) on rt
    return ask(root[rt], 1, 1e6, x);
}

void solve() {
    int n, k;
    cin >> n >> k;
    vector<int> a(k + 1), b(k + 1);
    for (int i = 1; i <= k; i++) {
        cin >> a[i];
    }
    for (int i = 1; i <= k; i++) {
        cin >> b[i];
    }
    vector<vector<int>> pass(n + 1); // node id
    vector<int> cur_pass(n + 1);
    int totid = 0;
    constexpr int N = 400100;
    vector<pair<int, int>> bel(N, {-1, -1}); // <path id, node id>
    vector<pair<int, int>> G(N, {-1, -1});
    for(int i = 1; i <= k; i++) {
        int p, x, w;
        cin >> p >> x;
        pass[x].push_back(totid);
        bel[totid] = {i, x};
        totid++;
        for(int j = 2; j <= p; j++) {
            cin >> w >> x;
            if(j > 1) G[totid - 1] = {totid, w};
            pass[x].push_back(totid);
            bel[totid] = {i, x};
            totid++;
        }
    }
    for(int i = 1; i <= n; i++) {
        sort(pass[i].begin(), pass[i].end(), [&](int p, int q) {
            return a[p] < a[q];
        });
    }
    constexpr ll inf = 1e18;
    vector<ll> dis(totid, inf);
    priority_queue<array<ll, 2>> pq; // <dis, x, type>
    for(auto id : pass[1]) {
        pq.push({dis[id] = 0, id});
    }
    modify(1, 0, 0);
    cur_pass[1] = pass[1].size();
    vector<int> vis(totid);
    while(pq.size()) {
        auto [d, x] = pq.top(); pq.pop();
        d = -d;
        if(vis[x]) continue;
        vis[x] = 1;
        auto [path_id, node_id] = bel[x];
        modify(node_id, b[path_id], d);
        while(cur_pass[node_id] < pass[node_id].size() && vis[pass[node_id][cur_pass[node_id]]]) {
            cur_pass[node_id]++;
        }
        if(cur_pass[node_id] < pass[node_id].size()) {
            int y = pass[node_id][cur_pass[node_id]];
            auto [y_path, y_node] = bel[y];
            auto res = query(node_id, a[y_path]);
            if(dis[y] > res) {
                dis[y] = res;
                pq.push({-dis[y], y});
            }
        }
        auto [y, w] = G[x];
        if(y != -1 && dis[y] > d + w) {
            dis[y] = d + w;
            pq.push({-dis[y], y});
        }
    }
    vector<ll> ans(n + 1, inf);
    for(int i = 1; i <= n; i++) {
        for(int j : pass[i]) {
            ans[i] = min(ans[i], dis[j]);
        }
    }
    for(int i = 2; i <= n; i++) {
        cout << ans[i] << " \n"[i == n];
    }
}
signed main() {
    ios::sync_with_stdio(false);
    cin.tie(0), cout.tie(0);
    int t = 1;
    // cin >> t;
    while (t--) solve();
    return 0;
}
/*
6 3
1 5 1
5 5 1
3 1 2 2 3 3
3 5 1 2 1 4
3 3 4 5 4 6
insert 1 5 0
insert 2 5 -2
y = 4    path = 2
query 2 5   23
insert 3 5 -1
y = 6    path = 3
query 3 1   4
insert 3 1 -4
y = 2    path = 3
query 3 1   -3
insert 5 1 0
y = 3    path = 5
query 5 3342445   3342445
insert 6 1 -4
insert 2 5 -23
insert 4 5 22
insert 5 5 -3342445
dis: 0 2 -3 3342445 -3342444 -22 4 0 4
-3342444 -3 -22 0 4

*/