#include<bits/stdc++.h>
using namespace std;
using ll = long long;
const int inf = 0x3f3f3f3f;
const int N = 3000+100;
int dp[2][N][2];
int main(){
    int n,k;cin>>n>>k;
    vector<vector<int> >vc(n+1);
    for(int i = 1; i <= n ;++i){
        int x;cin>>x;
        for(int j = 1; j<=x;++j){
            int tem;cin>>tem;
            vc[i].push_back(tem);
        }
    }// vc[i],体积为i+1，的价值

    int gu=1,gv=0;

    for(int i = 0;i<=k;++i)
        for(int j = 0 ;j<2;++j)
                dp[gu][i][j]=-inf;

    dp[gu][0][0] = 0;

    for(int i = 1; i<= n; ++i){
        gu^=1;gv^=1;
        for(int u = 0; u<= k ;++u){
            for(int j = 0 ; j<=1;++j){
                dp[gu][u][j] = dp[gv][u][j];
            }
        }
        for(int j=vc[i].size()-1;j>=vc[i].size()-1;--j){//用，用普通的，w_pi
            for(int u = 0;u<=k;++u){
                if(u+j+1<=k){
                    dp[gu][u+j+1][0] = max(dp[gu][u+j+1][0],dp[gv][u][0]+vc[i][j]);
                    dp[gu][u+j+1][1] = max(dp[gu][u+j+1][1],dp[gv][u][1]+vc[i][j]);
                }
            }
        }

        for(int j = vc[i].size()-2;j>=0;--j){//用了一次机会
            for(int u = 0;u<=k;++u){
                if(u+j+1<=k){
                    dp[gu][u+j+1][1] = max(dp[gu][u+j+1][1],dp[gv][u][0]+vc[i][j]);
                }
            }
        }
    }

    int ans = -inf;
    for(int i = 0;i<=k;++i)ans = max(ans,dp[gu][i][0]);

    cout<<max(ans,dp[gu][k][1]);

//    system("pause");


    return 0;

}