#include<iostream>
#include<vector>
#include<array>
#include<climits>
#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;
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);
	ll 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-1][j][0]);
				dp[i][j][1] = max(dp[i - 1][j - v[i][0]][1] + v[i][v[i][0]], dp[i-1][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]);
			}	
		}
	}
	int ans = 0;
	for (int i = 1; i <= n; i++)
	{
		for (int j = 0; j <= k; j++)
		{
			ans = max(ans, dp[i][j][0]);
		}
		ans = max(ans, dp[i][k][1]);
	}
}
void speed()
{
	ios::sync_with_stdio(0);
	cin.tie(0);                                                                                          
	cout.tie(0);
}
int main()
{
	speed();
	int t;
	//cin >> t;
	t = 1;
	while (t--)
	{
		solve();
	}
	return 0;
}