CF722F.Cyclic Cipher

You are given n sequences. Each sequence consists of positive integers, not exceeding m. All integers in one sequence are distinct, but the same integer may appear in multiple sequences. The length of the i-th sequence is k__i.

Each second integers in each of the sequences are shifted by one to the left, i.e. integers at positions i > 1 go to positions i - 1, while the first integers becomes the last.

Each second we take the first integer of each sequence and write it down to a new array. Then, for each value x from 1 to m we compute the longest segment of the array consisting of element x only.

The above operation is performed for 10100 seconds. For each integer from 1 to m find out the longest segment found at this time.

给你 $n$ 个序列。每个序列由不超过 $m$ 的正整数组成，同一序列中所有整数互不相同，但相同的整数可能出现在多个序列中。第 $i$ 个序列的长度为 $k_i$。

每一秒，每个序列中的整数均向左循环移动一位：即位置 $i\, (i > 1)$ 上的整数移动到位置 $i-1$，而原位置 $1$ 的整数则移至序列末尾（成为最后一个元素）。

每一秒，我们取出每个序列的第一个整数，并将它们依次写入一个新数组（该数组长度恒为 $n$）。接着，对每个值 $x$（从 $1$ 到 $m$），计算该数组中仅由元素 $x$ 构成的最长连续子段的长度。

上述操作持续进行 $10^{100}$ 秒。对每个从 $1$ 到 $m$ 的整数，求出在整个过程中该整数所对应的最长连续子段长度。

The first line of the input contains two integers n and m (1 ≤ n, m ≤ 100 000) — the number of sequences and the maximum integer that can appear in the sequences.

Then follow n lines providing the sequences. Each of them starts with an integer k__i (1 ≤ k__i ≤ 40) — the number of integers in the sequence, proceeded by k__i positive integers — elements of the sequence. It's guaranteed that all integers in each sequence are pairwise distinct and do not exceed m.

The total length of all sequences doesn't exceed 200 000.

输入的第一行包含两个整数 $n$ 和 $m$（$1 \leq n, m \leq 100\,000$）—— 分别表示序列的个数，以及序列中可能出现的最大整数值。

接下来是 $n$ 行，每行描述一个序列。每行以一个整数 $k_i$（$1 \leq k_i \leq 40$）开头，表示该序列中整数的个数；随后是 $k_i$ 个正整数，即该序列的元素。保证每个序列中的所有整数两两不同，且均不超过 $m$。

所有序列的总长度不超过 $200\,000$。

Print m integers, the i-th of them should be equal to the length of the longest segment of the array with all its values equal to i during the first 10100 seconds.

输出 m 个整数，其中第 i 个整数应等于在前 $10^{100}$ 秒内，数组中所有元素均等于 i 的最长连续段的长度。