A13942. Sum

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.