/*
    By: facug91
    From:
    Name:
    Date: 28/09/2015
*/

#include <bits/stdc++.h>
#define next asjkdbg1238dv8ydf38gy832gf8yd
#define prev asjkdbuiqdg783gdiu3dg79832dui
#define EPS 1e-9
#define MP make_pair
#define DB(x) cerr << "#" << (#x) << ": " << (x) << " "
#define DBL(x) cerr << "#" << (#x) << ": " << (x) << endl
const double PI = 2.0*acos(0.0);

#define INF 1000000000
#define MINUSINF -10000000000000ll// -10^13
#define MOD 1000000007ll
//#define MAXN 10000100

using namespace std;
typedef long long ll;
typedef pair<int, int> ii; typedef pair<int, ii> iii;
typedef vector<int> vi; typedef vector<ii> vii;     typedef vector<iii> viii;

ll n, m, len, DP[105][1005], acc[100005], big[100005];

int main () {
    ios_base::sync_with_stdio(0); cin.tie(0);
    //cout<<fixed<<setprecision(7); cerr<<fixed<<setprecision(7); //cin.ignore(INT_MAX, ' '); //cout << setfill('0') << setw(5) << 25
    int i, j, k;

    cin>>n>>m;
    memset(DP, 0, sizeof DP);
    for (i=1; i<=n; i++) {
        cin>>len;
        acc[0] = 0;
        for (j=1; j<=len; j++) {
            cin>>acc[j];
            acc[j] += acc[j-1];
        }
        big[0] = 0;
        for (j=1; j<=min(len, m); j++) {
            big[j] = 0;
            for (k=j; k<=len; k++) {
                big[j] = max(big[j], acc[k]-acc[k-j]);
            }
            //cerr<<"i "<<i<<" big["<<j<<"] "<<big[j]<<endl;
        }
        for (j=1; j<=m; j++) {
            for (k=0; k<=len; k++) {
                if (j-k < 0) DP[i][j] = max(DP[i][j], DP[i-1][j]);
                else DP[i][j] = max(DP[i][j], max(DP[i-1][j], DP[i-1][j-k]+big[k]));
            }
        }
    }
    cout<<DP[n][m]<<endl;

    return 0;
}