Sum
Description
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.
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.
Samples
3 3
2 5 10
3 1 2 3
2 1 20
26