CF1208E.Let Them Slide

You are given $n$ arrays that can have different sizes. You also have a table with $w$ columns and $n$ rows. The $i$-th array is placed horizontally in the $i$-th row. You can slide each array within its row as long as it occupies several consecutive cells and lies completely inside the table.

You need to find the maximum sum of the integers in the $j$-th column for each $j$ from $1$ to $w$ independently.

Optimal placements for columns $1$, $2$ and $3$ are shown on the pictures from left to right.

Note that you can exclude any array out of a column provided it remains in the window. In this case its value is considered to be zero.

给你 $n$ 个长度可能不同的数组。你还有一个具有 $w$ 列和 $n$ 行的表格。第 $i$ 个数组水平放置在第 $i$ 行中。你可以将每个数组在其所在行内左右滑动，只要它占据若干个连续的单元格，且完全位于表格内部即可。

你需要对每个 $j$（从 $1$ 到 $w$）独立地求出第 $j$ 列中所有整数之和的最大值。

从左到右依次展示了第 $1$、$2$ 和 $3$ 列的最优放置方式。

注意：对于某一列，你可以选择让任意一个数组不覆盖该列（只要该数组仍在表格窗口内），此时该数组在该列的贡献视为 $0$。

The first line contains two integers $n$ ($1 \le n \le 10^{6}$) and $w$ ($1 \le w \le 10^{6}$) — the number of arrays and the width of the table.

Each of the next $n$ lines consists of an integer $l_{i}$ ($1 \le l_{i} \le w$), the length of the $i$-th array, followed by $l_{i}$ integers $a_{i1}, a_{i2}, \ldots, a_{il_i}$ ($-10^{9} \le a_{ij} \le 10^{9}$) — the elements of the array.

The total length of the arrays does no exceed $10^{6}$.

第一行包含两个整数 $n$（$1 \le n \le 10^{6}$）和 $w$（$1 \le w \le 10^{6}$）——分别表示数组的个数以及表格的宽度。

接下来的 $n$ 行中，每行首先是一个整数 $l_{i}$（$1 \le l_{i} \le w$），表示第 $i$ 个数组的长度；随后是 $l_{i}$ 个整数 $a_{i1}, a_{i2}, \ldots, a_{il_i}$（$-10^{9} \le a_{ij} \le 10^{9}$）——表示该数组的元素。

所有数组的总长度不超过 $10^{6}$。

Print $w$ integers, the $i$-th of them should be the maximum sum for column $i$.

输出 $w$ 个整数，其中第 $i$ 个整数应为第 $i$ 列的最大和。

Illustration for the first example is in the statement.

第一个示例的示意图见题目描述中。