#include<bits/stdc++.h>
using namespace std;
const int INF=1e18;
using ll = long long;
void solve(){
	
	int n , k; cin >> n >> k;
	
	vector<vector<vector<ll>>> f(n + 1 , vector<vector<ll>>(k + 10 , vector<ll>(2)));
	vector<int>p (n + 1);
	vector<vector<int>> w(n + 1 , vector<int>(20));
	
	for(int i = 1 ; i <= n ; i++){
		cin >> p[i];
		for(int j = 1 ; j <= p[i] ; j++){
			cin >> w[i][j];
		}
	}
	
	//cout << '\n';
	for(int i = 1 ; i <= n ; i++){
		for(int j = k ; j >= 0 ; j--){
			f[i][j][0] = f[i - 1][j][0] , f[i][j][1] = f[i - 1][j][1];
			if(j + p[i] <= k){
				f[i][j + p[i]][0] = max(f[i][j + p[i]][0] , max(f[i - 1][j][1] , f[i - 1][j][0]) + w[i][p[i]]);
				f[i][j + p[i]][1] = max(f[i][j + p[i]][1] , f[i - 1][j][0] + w[i][p[i]]);
			}
			for(int q = 1 ; q + j <= k && q < p[i] ; q++){
				f[i][j + q][1] = max(f[i][j + q][1] , f[i - 1][j][0] + w[i][q]);
			}
		}
//		for(int j = k ; j >= 0 ; j--){
//			cout << j << ' ' << f[i][j][0] << ' ' << f[i][j][1] << '\n';
//		}
	}
	
	ll mx = 0;
	for(int i = 1 ; i <= n ; i++){
		
		for(int j = 0 ; j <= k ; j++){
			mx = max({mx , f[i][j][0] , f[i][j][1]});
		}
	}
	cout << mx << '\n';
	
}

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