/*
    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, elem, sum, tail, ans, DP[105][1005];
vector<ll> block[105], opt[105];

ll dp (int idx, int res) {
    if (idx == n) return 0ll;
    if (DP[idx][res] != -1) return DP[idx][res];
    ll ans = 0ll;
    for (int i=0; i<=min(res, (int)block[idx].size()); i++) {
        ans = max(ans, dp(idx+1, res-i) + opt[idx][i]);
    }
    return DP[idx][res] = ans;
}

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;
    for (i=0; i<n; i++) {
        cin>>len;
        block[i].push_back(0);
        for (j=1; j<=len; j++) {
            cin>>elem;
            block[i].push_back(elem);
            block[i][j] += block[i][j-1];
        }
        opt[i].push_back(0);
        for (j=1; j<=min(len, m); j++) {
            ans = 0;
            for (k=j; k<=len; k++) ans = max(ans, block[i][k]-block[i][k-j]);
            opt[i].push_back(ans);
        }
    }
    memset(DP, -1, sizeof DP);
    cout<<dp(0, m)<<endl;

    return 0;
}