#include<bits/stdc++.h>
#define ll long long
#define int long long
#define fr(i,j,k) for(register int i=j;i<=k;++i)
#define rf(i,j,k) for(register int i=j;i>=k;--i)
#define foredge(i,j) for(register int i=head[j];i;i=e[i].nxt)
#define randfind(l,r) (rand()%((r)-(l)+1)+(l))
#define pb push_back
#define Times printf("Time:%.3lf\n",clock()/CLOCKS_PER_SEC)
using namespace std;
inline int read(){
	int x=0;
	bool f=0;
	char c=getchar();
	while(!isdigit(c)) f|=(c=='-'),c=getchar();
	while(isdigit(c)) x=(x<<3)+(x<<1)+(c^48),c=getchar();
	return f?-x:x;
}
inline ll Read(){
	ll x=0;
	bool f=0;
	char c=getchar();
	while(!isdigit(c)) f|=(c=='-'),c=getchar();
	while(isdigit(c)) x=(x<<3)+(x<<1)+(c^48),c=getchar();
	return f?-x:x;
}
inline void write(int x){
    if(x<0){putchar('-');x=-x;}
    if(x>9)write(x/10);
    putchar(x%10+'0');
}
inline void writeln(int x){write(x); puts("");}
inline void writepl(int x){write(x); putchar(' ');}
inline void Write(ll x){
    if(x<0){putchar('-'); x=-x;}
    if(x>9)Write(x/10);
    putchar(x%10+'0');
}
inline void Writeln(ll x){Write(x); puts("");}
inline void Writepl(ll x){Write(x); putchar(' ');}
inline void gcd(int a,int b,int &d,int &x,int &y){
	if(!b){
		d=a;
		x=1;
		y=0;
	}
	else {
		gcd(b,a%b,d,y,x);
		y-=x*a/b;
	}
}
inline int china(int n,int *a,int *m){
	int M=1;
	int d,x=0,y;
	fr(i,0,n-1) M*=m[i];
	fr(i,0,n-1){
		int w=M/m[i];
		gcd(m[i],w,d,d,y);
		x=(x+y*w*a[i])%M;
	} 
	return (x+M)%M;
}
const int Maxc=9,Maxk=110,limit=10000;
set<int> value[Maxc];
int C,x[Maxc],k[Maxc],y[Maxc][Maxk];
inline void solve_enum(int s,int bc){
	fr(c,0,C-1){
		if(c!=bc){
			value[c].clear();
			fr(i,0,k[c]-1) value[c].insert(y[c][i]);
		}
	}
	for(int t=0;s!=0;++t){
		fr(i,0,k[bc-1]){
			int n=x[bc]*t+y[bc][i];
			if(n==0) continue;
			bool ok=1;
			fr(c,0,C-1) if(c!=bc){
				if(!value[c].count(n%x[c])){
					ok=0;
					break;
				}
			}
			if(ok){
				writeln(n);
				if(--s==0) break;
			}
		}
	}
}
int a[Maxc];
vector<int> sol;
inline void dfs(int dep){
	if(dep==C) sol.push_back(china(C,a,x));
	else {
		fr(i,0,k[dep]-1){
			a[dep]=y[dep][i];
			dfs(dep+1);
		}
	}
}
inline void solve_china(int s){
	sol.clear();
	dfs(0);
	sort(sol.begin(),sol.end());
	int M=1;
	fr(i,0,C-1) M*=x[i];
	vector<int> ans;
	for(int i=0;s!=0;++i){
		fr(j,0,sol.size()-1){
			int n=M*i+sol[j];
			if(n>0){
				writeln(n);
				if(--s==0) break;
			}
		}
	}
}
signed main(){
	freopen("UVA11754.out","w",stdout);
	int S;
	int cnt=0;
	while(1){
		C=read();
		S=read();
		if(!S && !C) break;
		++cnt;
//		printf("**%lld\n",cnt);
		int tot=1;
		int bestc=0;
		fr(c,0,C-1){
			x[c]=read();
			k[c]=read();
			tot*=k[c];
			fr(i,0,k[c]-1) y[c][i]=read();
			sort(y[c],y[c]+k[c]);
			if(k[c]*x[bestc]<k[bestc]*x[c]) bestc=c;
		}
		if(tot>limit) solve_enum(S,bestc);
		else solve_china(S);
		puts("");
	}
    // printf("\nTIME:%.3lf",(double)clock()/CLOCKS_PER_SEC);
	return 0;
}