Sum

Description:

Input:

The first line contains two integers $$$n$$$ and $$$k$$$ ($$$1 \le n, k \le 3\,000$$$): the number of arrays and operations.

Each of the next $$$n$$$ lines contain an array. The first integer in each line is $$$t_i$$$ ($$$1 \le t_i \le 10^6$$$): the size of the $$$i$$$-th array. The following $$$t_i$$$ integers $$$a_{i, j}$$$ ($$$0 \le a_{i, 1} \le \ldots \le a_{i, t_i} \le 10^8$$$) are the elements of the $$$i$$$-th array.

It is guaranteed that $$$k \le \sum\limits_{i=1}^n t_i \le 10^6$$$.

Output:

Print one integer: the maximum possible sum of all elements in Vasya's pocket after $$$k$$$ operations.

Sample Input:

3 3
2 5 10
3 1 2 3
2 1 20

Sample Output:

26