#include <bits/stdc++.h>
using namespace std;
using i64 = long long;
const i64 INF = 0x3f3f3f3f3f3f3f3f;

const int MAXN = 3010;
int n, k, p[MAXN];
i64 w[MAXN][20];

i64 dp[MAXN];
vector<int> not_select[MAXN];

void solve () {
    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 = k; j >= p[i]; --j) {
            if (dp[j] >= dp[j - p[i]] + w[i][p[i]]) {
                not_select[j].push_back(i);
            } else {
                dp[j] = dp[j - p[i]] + w[i][p[i]];
            }
        }
    }

    i64 ans = dp[k];
    for (int i = k - 1; i >= 0; --i) {
        int sp = k - i;
        for (auto j : not_select[i]) {
            if (sp < p[j]) ans = max(ans, dp[i] + w[j][sp]);
        }
    }

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

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

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

    return 0;
}