#include <bits/stdc++.h>

using namespace std;

int main(){
	ios::sync_with_stdio(false);

	int n,m, x;
	vector<vector<int>> shelfs, optansw, prefs, tabulardp;

	cin >> n >> m;
	shelfs.assign(n, vector<int>());
	prefs.assign(n, vector<int>());
	optansw.assign(n, vector<int>(101, 0));

	for(int i = 0; i < n; i++){
		cin >> x;
		shelfs[i].resize(x);
		prefs[i].resize(x+1); prefs[i][0] = 0;
		for(int j = 0; j < x; j++){
			cin >> shelfs[i][j];
			prefs[i][j+1] = prefs[i][j] + shelfs[i][j];
		}
	}

	for(int i = 0; i < n; i++){
		optansw[i][shelfs[i].size()] = prefs[i][shelfs[i].size()];
		for(int l = 0; l < shelfs[i].size(); l++){
			for(int r = l; r < shelfs[i].size(); r++){
				optansw[i][shelfs[i].size() - (r-l+1)] = max(optansw[i][shelfs[i].size() - (r-l+1)], prefs[i][shelfs[i].size()] - prefs[i][r+1] + prefs[i][l]);
			}
		}
		for(int l = shelfs[i].size()+1; l < 101; l++){
			optansw[i][l] = optansw[i][l-1];
		}
	}

	tabulardp.assign(n+1, vector<int>(m+1, 0));
	for(int i = 1; i <= n; i++){
		for(int j = 1; j <= m; j++){ // Descendo inicialmente j e pegando opt[0]
			int stop = min(100, j);
			for(int k = 0; k <= stop; k++){
				tabulardp[i][j] = max(tabulardp[i][j], tabulardp[i-1][j-k] + optansw[i-1][k]);
			}
		}
	}

	cout << tabulardp[n][m] << '\n';

	return 0;
}