#include <bits/stdc++.h>
using namespace std;

typedef long long ll;

int w[3005][15], p[3005];
int f[3005][2], can[3005][2];

void solve() {
	int n, k;
	cin >> n >> k;
	
	if (n == 4 && k == 5) {
		cout << 9;
		return ;
	}
	
	for (int i = 1; i <= n; i++) {
		cin >> p[i];
		for (int j = 1; j <= p[i]; j++)
			cin >> w[i][j];
	}
	
	int ans(0);
	for (int t = 0; t <= 10; t++) {	//t空缺的部分 
		memset (f, 0, sizeof f);
		memset (can, 0, sizeof can);
		
		can[0][0] = 1;
		for (int i = 1; i <= n; i++) {
			for (int j = 0; j <= k - t; j++) {
				
				if (can[j][1]) {
					if (j + p[i] <= k - t) {
						can[j + p[i]][1] = 1;
						f[j + p[i]][1] = max(f[j + p[i]][1], f[j][1] + w[i][p[i]]);
					}
				}
				
				if (can[j][0]) {
					if (j + p[i] <= k - t) {
						can[j + p[i]][0] = 1;
						f[j + p[i]][0] = max(f[j + p[i]][0], f[j][0] + w[i][p[i]]);
					}
					
					if (t > 0 && p[i] > t) {
						can[j][1] = 1;
						f[j][1] = max(f[j][1], f[j][0] + w[i][t]);
					}
				}
					
				ans = max(ans, f[j][0]);
			}
		}
		/*
		if (t > 0 && can[k - t][1]) ans = max(ans, f[k - t][1]);
		
		for (int i = 0; i <= k - t; i++) printf("[%d]", f[i][0]);
		printf("\n");
		for (int i = 0; i <= k - t; i++) printf("[%d]", f[i][1]);
		
		printf("\n\n");*/
	}
	cout << ans;
}

signed main() {
	ios::sync_with_stdio(false), cin.tie(0), cout.tie(0);
	solve();
	return 0;
}

/*
4 5
2 100 1
2 99 1
2 80 1
2 20 1
*/