#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define endl '\n'
typedef pair<int, int> PII;
const int N = 1e3 + 10;
const int mod = 1e9 + 7;
const int INF = 0x3f3f3f3f;
int T;
ll n, k;
ll f[N][N][1], p[N], w[N][10];
void solve()
{
    // code
    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];
        }
    }
    for (int i = 1; i <= n; i++)
    {
        for (int j = 1; j <= k; j++)
        {
            f[i][j][0] = f[i][j][1] = -INF;
        }
    }
    for (int i = 1; i <= n; i++)
    {
        for (int j = 1; j <= k; j++)
        {
            f[i][j][0] = max(f[i][j][0], f[i - 1][j][0]);
            f[i][j][1] = max(f[i][j][1], f[i - 1][j][1]);
            if (j >= p[i])
            {
                f[i][j][0] = max(f[i][j][0], f[i - 1][j - p[i]][0] + w[i][p[i]]);
                f[i][j][1] = max(f[i][j][1], f[i - 1][j - p[i]][1] + w[i][p[i]]);
            }
            for (int l = 1; l <= p[i]; l++)
            {
                if (j >= l)
                {
                    f[i][j][1] = max(f[i][j][1], f[i - 1][j - l][0] + w[i][l]);
                }
            }
        }
    }
    cout << max(f[n][k][0], f[n][k][1]) << '\n';
}
int main()
{
    ios::sync_with_stdio(false);
    cin.tie(0);
    cout.tie(0);

    int T = 1;
    // cin >> T;
    while (T--)
    {
        solve();
    }
    return 0;
}