CF1442D.Sum

普及/提高-

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题目描述

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.

输入格式

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

输出格式

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

输入输出样例

输入#1
```
3 3
2 5 10
3 1 2 3
2 1 20
```
输出#1
```
26
```

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