#include<bits/stdc++.h>
#include<unordered_map>
#include<unordered_set>
typedef long long ll;
typedef long double ld;
typedef unsigned long long ull;
#define debug(a) cout<<a<<'\n'
#define Pll pair<ll,ll>
#define PII pair<int,int>
#define ft first
#define sd second
#define vec vector
#define pushk push_back
#define ump unordered_map
#define pl p<<1
#define pr p<<1|1
using namespace std;
const int N = 3e3 + 10, M = 2e6 + 10, mod = 1e9+7;
const ll inf = 1e18;
const ld eps = 1e-13;
int mov[4][2] = { {0,1},{1,0},{-1,0},{0,-1} }, dx, dy, _ = 1, __ = 1;
void bout(bool f) {
	if (f)cout << "YES\n";
	else cout << "NO\n";
}
ll n,m,k;
int pre[N][N],suf[N][N],np[N][15];

void ini() {

}
void solve() {
	cin>>n>>k;
	int x,y,z,w,v,p,sp=0;
	for(int i=1;i<=n;++i){
		cin>>np[i][0];
		sp+=np[i][0];
		for(int j=1;j<=np[i][0];++j)cin>>np[i][j];
	}
	memset(pre,0xcf,sizeof pre);
	memset(suf,0x3f,sizeof suf);
	pre[0][0]=suf[n+1][0]=0;
	for(int i=1;i<=n;++i){
		p=np[i][0];
		w=np[i][p];
		for(int j=1;j<=k;++j){
			if(j>=p)pre[i][j]=max(pre[i-1][j],pre[i-1][j-p]+w);
			else pre[i][j]=pre[i-1][j];
		}
	}
	for(int i=n;i>=1;--i){
		p=np[i][0];
		w=np[i][p];
		for(int j=1;j<=k;++j){
			if(j>=p)suf[i][j]=max(suf[i+1][j],suf[i+1][j-p]+w);
			else suf[i][j]=suf[i+1][j];
		}
	}
	int ans=0;
	if(sp<=k)ans=pre[n][sp];
	for(int i=1;i<=n;++i){
		p=np[i][0];
		for(int V=k-p+1;V<k;++V){
			w=np[i][k-V];
			for(int j=0;j<=V;++j){
				ans=max(ans,pre[i-1][j]+suf[i+1][V-j]+w);
			}
		}
	}
	cout<<ans;
}

int main() {
	ios::sync_with_stdio(0);
	cin.tie(0);
	cout.tie(0);
#ifndef ONLINE_JUDGE
	streambuf *cinbp=cin.rdbuf(),*coutbp=cout.rdbuf();
	ifstream fin("in.txt");
	ofstream fout("out.txt");	
	cin.rdbuf(fin.rdbuf());
	cout.rdbuf(fout.rdbuf());
#endif
	//cin >> _;
	__ = _;
	ini();
	while (_--) {
		solve();
	}
	return 0;
}