D. Sum
time limit per test
1.5 seconds
memory limit per test
512 megabytes
standard input
standard output

You are given $$$n$$$ non-decreasing arrays of non-negative numbers.

Vasya repeats the following operation $$$k$$$ times:

  • Selects a non-empty array.
  • Puts the first element of the selected array in his pocket.
  • Removes the first element from the selected array.

Vasya wants to maximize the sum of the elements in his pocket.


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


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

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