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

const int N=3005;
int f[N][2],g[N][2],n,m,a[N][15],p[N],sump[N];
bitset<3001> cpo[N];

signed main(){
	ios::sync_with_stdio(0);
	cin>>n>>m;
	for(int i=1;i<=n;i++){
		cin>>p[i];
		for(int j=1;j<=p[i];j++) cin>>a[i][j];
		sump[i]=sump[i-1]+p[i];
	}
	if(sump[n]<=m){
		int ans=0;
		for(int i=1;i<=n;i++) ans+=a[i][p[i]];
		cout<<ans;
		return 0;
	}
	cpo[n+1][0]=1;
	for(int i=n;i;i--){
		cpo[i]=cpo[i+1]|(cpo[i+1]<<p[i]);
	}
	memset(f,-60,sizeof f);
	memset(g,-60,sizeof g);
	f[0][0]=0;
	for(int i=1;i<=n;i++){
		for(int j=0;j<=m;j++) for(int o:{0,1}) if(j>=p[i]){
			g[j][o]=max(g[j][o],f[j-p[i]][o]+a[i][p[i]]);
		}
		for(int k=1;k<=p[i];k++) for(int j=k;j<=m;j++) if(cpo[i+1][m-j]){
			g[j][1]=max(g[j][1],f[j-k][0]+a[i][k]);
		}
		memcpy(f,g,sizeof f);
	}
	cout<<f[m][1];
}