#include <bits/stdc++.h>
#define int long long
#define x first
#define y second
#define bug(X) cout << "bug:# " << X << endl
#define bug2(f, X) cout << "bug:# " << f << " " << X << endl
#define bug3(i, j, G) cout << "bug:# " << i << ' ' << j << ' ' << G << endl
#define endl '\n'
using namespace std;
const int mod = 998244353;
const int N = 10 + 5e5;
void _();
signed main()
{
    ios::sync_with_stdio(0);
    cin.tie(0);
    cout.tie(0);
    int t = 1;
    // cin >> t;
    while (t--)
        _();
    return 0;
}

void _()
{
    int n, k;
    cin >> n >> k;
    int sum = 0;
    vector<int> p(n + 1);
    vector<array<int, 11>> w(n + 1);
    for (int i = 1; i <= n; i++)
    {
        cin >> p[i];
        sum += p[i];
        for (int j = 1; j <= p[i]; j++)
            cin >> w[i][j];
    }

    vector<vector<int>> f(k + 1, vector<int>(2, -1e17));
    f[0][0] = 0;
    // vector<vector<int>> f(k+1,vector<int>(2));
    for (int i = 1; i <= n; i++)
        for (int j = k; j; j--)
        {
            if (j >= p[i])
            {
                f[j][1] = max(f[j][1], f[j - p[i]][1] + w[i][p[i]]);
                f[j][0] = max(f[j][0], f[j - p[i]][0] + w[i][p[i]]);
            }
            for (int k = 1; k < p[i]; k++)
                if (j >= k)
                    f[j][1] = max(f[j][1], f[j - k][0] + w[i][k]);
        }

    int res = max(f[k][1], f[k][0]);
    // if (sum < k)
    //     res = f[sum][0];
        // if(sum<k) bug2(f[sum][0],max(f[k][1],f[k][0]));
    cout << res << endl;
}