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

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.

Example
Input
3 3
2 5 10
3 1 2 3
2 1 20

Output
26