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

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

i64 dp[MAXN][2], sum = 0;

void solve () {
    cin >> n >> k;
    for (int i = 1; i <= n; ++i) {
        cin >> p[i];
        sum += p[i];
        for (int j = 1; j <= p[i]; ++j) {
            cin >> w[i][j];
        }
    }

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

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

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

    if (sum <= k) cout << dp[k][0] << "\n";
    else cout << max(dp[k][0], dp[k][1]) << "\n";
}

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

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

    return 0;
}