#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const int N = 410000;
const ll INF = 1e18;
int n, m;
int a[N], b[N];
int t, to[N], id[N];
vector<pair<int, int>> e[N];
vector<int> v[N];
deque<int> st[N];
int stp[N];
ll dis[N];
bool vis[N];
ll ans[N];
inline ll calc(int x, int y)
{
    return dis[x] + 1ll * a[id[y]] * b[id[x]];
}
inline double slope(int x, int y)
{
    if (b[id[x]] == b[id[y]])
        return INF * (dis[x] > dis[y]);
    if (dis[x] == dis[y])
        return INF * (b[id[x]] > b[id[y]]);
    return -1.0 * (b[id[x]] - b[id[y]]) / (dis[x] - dis[y]);
}
int main()
{
    scanf("%d%d", &n, &m);
    for (int i = 1; i <= m; i++)
        scanf("%d", &a[i]);
    for (int i = 1; i <= m; i++)
        scanf("%d", &b[i]);
    for (int i = 1; i <= m; i++)
    {
        int siz;
        scanf("%d", &siz);
        int lst;
        {
            int x;
            scanf("%d", &x);
            t++, to[t] = x, id[t] = i;
            v[x].push_back(t);
            lst = t;
        }
        for (int j = 2; j <= siz; j++)
        {
            int w, x;
            scanf("%d%d", &w, &x);
            t++, to[t] = x, id[t] = i;
            e[lst].push_back(make_pair(t, w));
            v[x].push_back(t);
            lst = t;
        }
    }
    for (int i = 1; i <= n; i++)
    {
        sort(v[i].begin(), v[i].end(), [](const int x, const int y)
             { return a[id[x]] < a[id[y]]; });
    }
    priority_queue<pair<ll, int>, vector<pair<ll, int>>, greater<pair<ll, int>>> pq;
    for (int i = 1; i <= t; i++)
        if (to[i] == 1)
            pq.push(make_pair(0, i));
        else
            dis[i] = INF;
    for (int i = 1; i <= n; i++)
        ans[i] = INF;
    while (pq.empty() == 0)
    {
        int x = pq.top().second;
        int tmp = pq.top().first;
        pq.pop();
        if (vis[x])
            continue;
        vis[x] = 1;
        int i = to[x];
        dis[x] = tmp;
        ans[i] = min(ans[i], dis[x]);
        while (stp[i] < (int)v[i].size() && vis[v[i][stp[i]]])
            stp[i]++;
        if (stp[i] < (int)v[i].size())
        {
            int y = v[i][stp[i]];
            while (st[i].size() > 1 && slope(st[i][st[i].size() - 2], st[i].back()) < slope(st[i].back(), x))
                st[i].pop_back();
            st[i].push_back(x);
            while (st[i].size() > 1 && calc(st[i][0], y) > calc(st[i][1], y))
                st[i].pop_front();
            if (calc(st[i][0], y) < dis[y])
                pq.push(make_pair(calc(st[i][0], y), y));
        }
        for (auto pr : e[x])
        {
            int y = pr.first, z = pr.second;
            if (dis[x] + z < dis[y])
                pq.push(make_pair(dis[x] + z, y));
        }
    }
    for (int i = 2; i <= n; i++)
        printf("%lld ", ans[i]);
    return 0;
}