CF1442D 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.