#include<bits/stdc++.h>
#define ll long long

using namespace std;

const int N = 3e3 + 10, INF = 1e9 + 7;
int n, k, f[N][N], g[N][N];
vector<int>e[N];

void solve()
{
    cin >> n >> k;
    for (int i = 1; i <= n; i++)
    {
        int t; cin >> t;
        while (t--) {
            int x; cin >> x; e[i].push_back(x);
        }
    }
    for (int i = 1; i <= k; i++)g[0][i] = f[0][i] = -INF;
    for (int i = 1; i <= n; i++)
    {
        for (int j = 0; j <= k; j++)g[i][j] = g[i - 1][j], f[i][j] = g[i - 1][j];
        int p = e[i].size();
        for (int j = p; j <= k; j++)f[i][j] = max(f[i][j], f[i - 1][j - p] + e[i].back()), g[i][j] = max(g[i][j], g[i - 1][j - p] + e[i].back());
        for (int s = 1; s <= p; s++)
        {
            for (int j = s; j <= k; j++)g[i][j] = max(g[i][j], f[i - 1][j - s] + e[i][s - 1]);
        }
    }
    cout << g[n][k] << '\n';
}

int main()
{
    ios::sync_with_stdio(0), cin.tie(0), cout.tie(0);
    int t = 1;
    while (t--)solve();
    return 0;
}