#include <bits/stdc++.h>
using namespace std;
using i64 = long long;
const i64 INF = 1e18;

void solve () {
    int n, k;
    cin >> n >> k;

    vector<int> p(n + 1, 0);
    vector<vector<i64>> w(n + 1);
    i64 s = 0;

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

    if (s <= k) {
        i64 ans = 0;
        for (int i = 1; i <= n; ++i) {
            ans += w[i][p[i]];
        }
        cout << ans << "\n";
        return;
    }

    vector<vector<array<i64, 2>>> dp(n + 1, vector<array<i64, 2>>(k + 1, {-INF, -INF}));
    dp[0][0][0] = 0;

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

            if (j >= p[i]) {
                dp[i][j][0] = max(dp[i][j][0], dp[i - 1][j - p[i]][0] + w[i][p[i]]);
                dp[i][j][1] = max(dp[i][j][1], dp[i - 1][j - p[i]][1] + w[i][p[i]]);
            }

            for (int t = 1; t <= min(j, p[i] - 1); ++t) {
                dp[i][j][1] = max(dp[i][j][1], dp[i - 1][j - t][0] + w[i][t]);
            }
        }
    }

    cout << dp[n][k][1] << "\n";
}

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

    int t = 1;
    // cin >> t;
    while (t--) {
        solve ();
    }

    return 0;
}