#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const int N=210000;
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]];
}
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 b[id[x]]<b[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;
		pq.pop();
		if(vis[x])
			continue;
		vis[x]=1;
		int i=to[x];
		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(stp[i]<(int)v[i].size()&&st[i].empty()==0&&calc(x,y)<calc(st[i].back(),y))
				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(dis[y]=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[y]=dis[x]+z,y));
		}
	}
	for(int i=2;i<=n;i++)
		printf("%lld ",ans[i]);
	return 0;
}