#include <iostream>
#include <algorithm>
#include <cstring>
using namespace std;
const int N = 3015;
int dp[N][N][2], n, k, w[N][11], p[N], res;
signed main()
{
    ios::sync_with_stdio(false), cin.tie(0), cout.tie(0);
    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 = 0; j <= k; j++)
        {
            dp[i][j][0] = max(dp[i][j][0], dp[i - 1][j][0]);
            dp[i][j][1] = max(dp[i][j][1], dp[i - 1][j][1]);
            if (j >= p[i])
            {
                dp[i][j][1] = max(dp[i][j][1], dp[i - 1][j - p[i]][1] + w[i][p[i]]);
                dp[i][j][0] = max(dp[i][j][0], dp[i - 1][j - p[i]][0] + w[i][p[i]]);
            }
            for (int tmp = 1; tmp <= p[i]; tmp++)
                if (j >= tmp)
                    dp[i][j][1] = max(dp[i][j][1], dp[i][j - tmp][0] + w[i][tmp]);
        }
    }
    for (int i = 1; i <= n; i++)
        for (int j = 0; j <= k; j++)
        {
            res = max(res, dp[i][j][0]);
            if (j == k)
                res = max(res, dp[i][j][1]);
        }
    cout << res << endl;
}