#include <bits/stdc++.h>
using namespace std;
template <typename T>inline void read(T &x)
{
    x=0;char c=getchar();bool f=0;
    for(;c<'0'||c>'9';c=getchar())f|=(c=='-');
    for(;c>='0'&&c<='9';c=getchar())x=(x<<1)+(x<<3)+(c-'0');
    x=(f?-x:x);
}
const int N = 1005;
const int M = 1005;
vector<int> transport[N];
int K[M];
vector<int> seq[M];
vector<int> G[N];
int dfn[N],low[N],ins[N],num=0;
vector<int> scc[N];
stack<int> st;
int bel[N],cnt=0;
int n,m;
void tarjan(int x)
{
	dfn[x]=low[x]=++num;
	st.push(x);
	ins[x]=1;
	for(int y:G[x])
	{
		if(!dfn[y])
		{
			tarjan(y);
			low[x]=min(low[x],low[y]);
		}
		else if(ins[y])
		{
			low[x]=min(low[x],dfn[y]);
		}
	}
	if(dfn[x]==low[x])
	{
		cnt++;
		int y;
		do
		{
			y=st.top();
			st.pop();
			ins[y]=0;
			bel[y]=cnt;
			scc[cnt].push_back(y);
		}while(x!=y);
	}
}
int tim[N],ord[N],pos[N],tot=0;
int deg[N];
vector<int> T[N];
typedef long long LL;
LL f[N][N],S[N],C[N];
int type[N];
LL Ans[N];
void solve(int x)
{
    f[x][x]=1;
    for(int i=pos[x]-1;i>=1;i--)
    {
        int u=ord[i];
        for(int y:scc[u])
        for(int j:transport[y])
        if(type[j]==4)
        {
            LL sum=0;
            for(int z:seq[j])
            sum+=f[bel[z]][x];
            f[u][x]=max(f[u][x],sum);
        }
    }
    for(int i=1;i<=tot;i++)
    Ans[x]+=f[i][x]*S[i];
}
int fro[N];
bool inf[N];
int main()
{
    read(n);read(m);
    for(int i=1;i<=n;i++)read(C[i]);
    for(int i=1;i<=m;i++)
    {
        int x;
        read(x);
        fro[i]=x;
        read(K[i]);
        for(int j=1;j<=K[i];j++)
        {
            int y;
            read(y);
            seq[i].push_back(y);
            G[x].push_back(y);
        }
        transport[x].push_back(i);
    }
    queue<int> q;
    for(int i=1;i<=n;i++)
    if(!dfn[i])tarjan(i);
    for(int i=1;i<=n;i++)S[bel[i]]+=C[i];
    for(int x=1;x<=n;x++)
    for(int y:G[x])
    {
        if(bel[x]!=bel[y])
        {
            T[bel[x]].push_back(bel[y]);
            deg[bel[y]]++;
        }
    }
    for(int i=1;i<=m;i++)
    {
        bool flag=1,flag2=0;
        int s=fro[i];
        for(int y:seq[i])flag&=(bel[s]==bel[y]),flag2|=(bel[s]==bel[y]);
        if(flag&&K[i]==1)type[i]=1;
        else if(flag)type[i]=2;
        else if(flag2)type[i]=3;
        else type[i]=4;
    }
    for(int i=1;i<=cnt;i++)if(!deg[i])q.push(i);
    while(!q.empty())
    {
        int x=q.front();
        ord[++tot]=x;
        pos[x]=tot;
        q.pop();
        for(int y:T[x])
        {
            deg[y]--;
            if(!deg[y])q.push(y);
        }
    }
    for(int x=1;x<=cnt;x++)
    {
        solve(x);
    }
    for(int u=1;u<=tot;u++)
    if(Ans[u]>0)
    {
        for(int y:scc[u])
        for(int i:transport[y])
        if(type[i]==2)inf[u]=1;
        else if(type[i]==3)
        {
            for(int z:seq[i])
            if(bel[z]!=u)inf[bel[z]]=1;
        }
    }
    for(int i=1;i<=tot;i++)if(inf[i])q.push(i);
    while(!q.empty())
    {
        int x=q.front();
        q.pop();
        for(int y:T[x])
        {
            if(!inf[y])
            {
                inf[y]=1;
                q.push(y);
            }
        }
    }
    for(int i=1;i<=n;i++)
    {
        if(inf[bel[i]])printf("infinity\n");
        else printf("%lld\n",Ans[bel[i]]);
    }
    return 0;
}