#include <bits/stdc++.h>
using namespace std;

#define int LL
using LL = long long;
using ll = long long;
constexpr int N = 3010;
constexpr LL inf = 1E18;

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

    int n, k;
    cin >> n >> k;

    vector<vector<int>> w(n + 1);
    vector<int> p(n + 1);

    for (int i = 1; i <= n; i++) {
        cin >> p[i];
        w[i].resize(p[i] + 1);
        for (int j = 1; j <= p[i]; j++) {
            cin >> w[i][j];
        }
    }

    if (k == 0) {
        cout << 0 << "\n";
        return 0;
    }

    vector<array<LL, N>> pre(n + 1);
    for (int i = 0; i <= n; i++) {
        fill(pre[i].begin(), pre[i].end(), -inf);
        pre[i][0] = 0;
    }
    for (int i = 1; i <= n; i++) {
        for (int j = p[i]; j < N; j++) {
            pre[i][j] = max(pre[i - 1][j], pre[i - 1][j - p[i]] + w[i].back());
        }
    }

    // for (int i = 1; i <= n; i++) {
    //     for (int j = 0; j <= 10; j++) {
    //         cout << pre[i][j] << " ";
    //     }
    //     cout << "\n";
    // }

    vector<array<LL, N>> suf(n + 2, array<LL, N>{});
    for (int i = 0; i <= n + 1; i++) {
        fill(suf[i].begin(), suf[i].end(), -inf);
        suf[i][0] = 0;
    }
    for (int i = n; i >= 1; i--) {
        for (int j = p[i]; j < N; j++) {
            suf[i][j] = max(suf[i + 1][j], suf[i + 1][j - p[i]] + w[i].back());
        }
    }

    LL ans = 0;
    for (int i = 1; i < N; i++) {
        ans = max(ans, pre[n][i]);
    }

    for (int i = 1; i <= n; i++) {
        LL dp[11] = {};
        for (int s = 0; s <= 10; s++) {
            for (int j = 0; j <= k; j++) {
                if (k - s - j < 0) continue;
                dp[s] = max(dp[s], pre[i - 1][j] + suf[i + 1][k - s - j]);
            }
        }
        for (int j = 1; j < p[i]; j++) {
            ans = max(ans, dp[j] + w[i][j]);
        }
    }

    cout << ans << "\n";
}