#include<bits/stdc++.h>
using namespace std;
#define ll long long
#define MP make_pair
mt19937 rnd(time(0));
const int MAXN=3005;
ll f[MAXN][MAXN],g[MAXN][MAXN];
int n,k,s,p[MAXN];ll w[MAXN][15];
int main(){
	ios::sync_with_stdio(false);
	cin>>n>>k;
	for(int i=1;i<=n;i++){
		cin>>p[i];
		for(int j=1;j<=p[i];j++) cin>>w[i][j];
		s+=p[i];
	}
	if(s<=k){
		ll ans=0;
		for(int i=1;i<=n;i++) ans+=w[i][p[i]];
		cout<<ans<<endl;return 0;
	}
	memset(f,-0x3f,sizeof(f));memset(g,-0x3f,sizeof(g));
	f[0][0]=0;
	auto cmax=[&](ll &x,ll y){if(x<y)x=y;}; 
	for(int i=1;i<=n;i++){
		for(int j=p[i];j<=k;j++){
			cmax(f[i][j],f[i-1][j]);cmax(f[i][j],f[i-1][j-p[i]]+w[i][p[i]]);
			cmax(g[i][j],g[i-1][j]);cmax(g[i][j],g[i-1][j-p[i]]+w[i][p[i]]);
		}
		for(int j=1;j<=p[i];j++) for(int t=j;t<=k;t++){
			cmax(g[i][t],f[i-1][t-j]+w[i][j]);
		}
	}
	cout<<g[n][k]<<endl;
	return 0;
}