#include<iostream>
#include<vector>
#include<array>
#include<random>
#include<queue>
#include<algorithm>
#include<cmath>
using namespace std;
//typedef long long ll;
typedef long double ld;
typedef unsigned int ui;
typedef pair<int, int> pii;
constexpr int inf = 1e9;
typedef long long int;
void solve()
{
int n, k;
cin >> n >> k;
vector<vector<array<int, 2>>>dp(n + 1, vector<array<int, 2>>(k + 1, { -inf, -inf }));
vector<array<int, 11>>v(n + 1);
int sum = 0;
for (int i = 1; i <= n; i++)
{
cin >> v[i][0];
for (int j = 1; j <= v[i][0]; j++)
{
cin >> v[i][j];
}
sum += v[i][v[i][0]];
}
if (sum <= k)
{
cout << sum << endl;
return;
}
dp[0][0][0] = 0;
dp[0][0][1] = 0;
for (int i = 1; i <= n; i++)
{
for (int j = 0; j <= k; j++)
{
dp[i][j][0] = dp[i - 1][j][0];
dp[i][j][1] = dp[i - 1][j][1];
if (j >= v[i][0])
{
dp[i][j][0] = max(dp[i - 1][j - v[i][0]][0] + v[i][v[i][0]], dp[i][j][0]);
dp[i][j][1] = max(dp[i - 1][j - v[i][0]][1] + v[i][v[i][0]], dp[i][j][1]);
}
for (int k = 1; k < v[i][0] && j >= k; k++)
{
dp[i][j][1] = max(dp[i - 1][j - k][0] + v[i][k], dp[i][j][1]);
}
}
}
cout << max(dp[n][k][1],dp[n][k][0]) << endl;
}
void speed()
{
ios::sync_with_stdio(0);
cin.tie(0);
cout.tie(0);
}
signed main()
{
speed();
int t;
//cin >> t;
t = 1;
while (t--)
{
solve();
}
return 0;
}