#include <iostream>
#include <vector>
#include <algorithm>
using namespace std;

const int N = 3001;
int dp[N][N][2]; // 0/1:是否"已满"
int v[N][11];
int w[N];

void solve(istream &in, ostream &out) {
    int n, m;
    in >> n >> m;
    int tot = 0;
    for (int i = 1; i <= n; ++i) {
        in >> w[i];
        tot += w[i];
        for (int j = 1; j <= w[i]; ++j) {
            in >> v[i][j];
        }
    }

    if (m >= tot) {
        int ans = 0;
        for (int i = 1; i <= n; ++i) {
            ans += v[i][w[i]];
        }
        out << ans << endl;
        return;
    }

    for (int i = 0; i <= n; ++i) {
        for (int j = 0; j <= m; ++j) {
            dp[i][j][0] = -1e9;
            dp[i][j][1] = -1e9;
        }
    }
    dp[0][0][0] = dp[0][0][1] = 0;

    for (int i = 1; i <= n; ++i) {
        for (int j = 0; j <= m; ++j) {
            dp[i][j][0] = dp[i-1][j][0];
            dp[i][j][1] = dp[i-1][j][1];

            if (j >= w[i]) {
                // "非满"
                dp[i][j][0] = max(dp[i][j][0], dp[i-1][j-w[i]][0] + v[i][w[i]]);

                // "之前就已满"
                dp[i][j][1] = max(dp[i][j][1], dp[i-1][j-w[i]][1] + v[i][w[i]]);
            }

            // "此时进行已满操作"
            for (int k = 1; k <= w[i]-1; ++k) {
                if (j >= k) {
                    dp[i][j][1] = max(dp[i][j][1], dp[i-1][j-k][0] + v[i][k]);
                }
            }
        }
    }
    int ans = max(dp[n][m][1], dp[n][m][0]);
    out << ans << endl;
}

int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    cout.tie(nullptr);

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