#include<bits/stdc++.h>
using namespace std;
#define int long long
#define db double
const int N=3e5+5;
const int M=3e3+5;
const int INF=1e9+7;

int n,k;
int f1[M][M][2]={0};
int f2[M][M][2]={0};
int p[M],w[M][M];

void solve()
{
	cin>>n>>k;
	for(int i=1;i<=n;i++){
		cin>>p[i];
		for(int j=1;j<=p[i];j++){
			cin>>w[i][j];
		}
	}
    for(int i=1;i<=k;i++){
        f1[0][i][0]=f1[0][i][1]=-INF;
        f2[n+1][i][0]=f2[n+1][i][1]=-INF;
    }
	for(int i=1;i<=n;i++){
		for(int j=0;j<=k;j++){
			f1[i][j][0]=max(f1[i-1][j][1],f1[i-1][j][0]);
            if(j>=p[i])
			    f1[i][j][1]=max(f1[i-1][j-p[i]][1],f1[i-1][j-p[i]][0])+w[i][p[i]];
		}
	}
	for(int i=n;i>=1;i--){
		for(int j=0;j<=k;j++){
			f2[i][j][0]=max(f2[i+1][j][1],f2[i+1][j][0]);
            if(j>=p[i])
			    f2[i][j][1]=max(f2[i+1][j-p[i]][1],f2[i+1][j-p[i]][0])+w[i][p[i]];
		}
	}
	int ans=-INF;
	for(int i=0;i<=k;i++){
		ans=max(ans,max(f1[n][i][1],f1[n][i][0]));
	}
	for(int i=1;i<=n;i++){
		for(int pp=1;pp<p[i];pp++){
			int temp=0;
			for(int j=0;j<=k-pp;j++){
				temp=max(temp,f1[i][j][0]+f2[i][k-pp-j][0]);
				temp=max(temp,f2[i][j][0]+f1[i][k-pp-j][0]);
			}
			ans=max(ans,temp+w[i][pp]);
		}
	}
	cout<<ans<<endl;
}
signed main()
{
    ios::sync_with_stdio(false);
    cin.tie(0);
    int T = 1;
    // cin >> T;
    while (T--) {
        solve();
    }
    return 0;
}
/*
*/