#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][MAXN][2];
i64 mx[MAXN][2];

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

    cout << max(dp[n][k][0], 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;
}