#include<bits/stdc++.h>
#define irep(i,l,r) for(int (i) = (l); (i) <= (r); ++(i))
#define drep(i,r,l) for(int (i) = (r); (i) >= (l); --(i))
#define ceil(pp,qq) (((pp)>0)^((qq)>0)?-abs(pp)/abs(qq):(pp)%(qq)?(pp)/(qq)+1:(pp)/(qq))
#define floor(pp,qq) (((pp)>0)^((qq)>0)?-ceil(abs(pp),abs(qq)):(pp)/(qq))
#define ll long long
#define LL __int128
using namespace std;

inline ll read(){
	char ch = getchar();
	ll s = 0; bool w = 0;
	while(!isdigit(ch)){if(ch == '-')w = 1;ch = getchar();}
	while(isdigit(ch))s = (s << 3) + (s << 1) + (ch ^ 48), ch = getchar();
	return w ? - s : s;
}

inline char rc(){
	char ch = getchar();
	while(1){
		if(ch >= 'A' && ch <= 'Z')return ch;
		if(ch >= 'a' && ch <= 'z')return ch;
		ch = getchar();
	}
}

template<class T1, class T2>
T1 min(T1 AA, T2 BB){return AA > BB ? BB : AA;}
template<class T1, class T2>
T1 max(T1 AA, T2 BB){return AA < BB ? BB : AA;}

const int itinf = 1e9;
const ll llinf = 4e18;
const int mod = 1000000007;
const int N = 500009;
int f[3005][3005][2];
int main(){
	int n = read(), m = read();
	if(m == 0){
		putchar('0');
		return 0;
	}
	memset(f, -10, sizeof(f));
	f[0][0][0] = f[0][0][1] = 0;
	irep(i,1,n){
		int pi = read();
		vector<int>w(pi + 1);
		irep(j,1,pi)w[j] = read();
		for(int pt = 1; pt <= pi; ++ pt){
			for(int wt = 0; wt + pt <= m; ++ wt){
				f[i][wt + pt][1] = max({
				f[i - 1][wt + pt][1],
				f[i - 1][wt][0] + w[pt],
				f[i][wt + pt][1]
				});
			}
		}
		for(int wt = 0; wt + pi <= m; ++ wt){
			for(int is = 0; is <= 1; ++ is){
				f[i][wt + pi][is] = max({f[i][wt + pi][is], f[i - 1][wt + pi][is], f[i - 1][wt][is] + w[pi]});
				f[i][wt][is] = max(f[i - 1][wt][is], f[i][wt][is]);
			}
		}
	}
	cout << max(f[n][m][1], f[n][m][0]);
	return 0;
}