CF1166E.The LCMs Must be Large

Dora the explorer has decided to use her money after several years of juicy royalties to go shopping. What better place to shop than Nlogonia?

There are $n$ stores numbered from $1$ to $n$ in Nlogonia. The $i$-th of these stores offers a positive integer $a_i$.

Each day among the last $m$ days Dora bought a single integer from some of the stores. The same day, Swiper the fox bought a single integer from all the stores that Dora did not buy an integer from on that day.

Dora considers Swiper to be her rival, and she considers that she beat Swiper on day $i$ if and only if the least common multiple of the numbers she bought on day $i$ is strictly greater than the least common multiple of the numbers that Swiper bought on day $i$.

The least common multiple (LCM) of a collection of integers is the smallest positive integer that is divisible by all the integers in the collection.

However, Dora forgot the values of $a_i$. Help Dora find out if there are positive integer values of $a_i$ such that she beat Swiper on every day. You don't need to find what are the possible values of $a_i$ though.

Note that it is possible for some values of $a_i$ to coincide in a solution.

探险家朵拉在获得了多年丰厚的版税收入后，决定去购物。还有什么地方比 Nlogonia 更适合购物呢？

Nlogonia 共有 $n$ 家商店，编号从 $1$ 到 $n$。第 $i$ 家商店提供一个正整数 $a_i$。

在最近的 $m$ 天中，朵拉每天都会从其中某家商店购买一个整数。同一天，狐狸斯威珀则会从朵拉当天未购买整数的所有商店中，各购买一个整数。

朵拉视斯威珀为自己的竞争对手；她认为自己在第 $i$ 天战胜了斯威珀，当且仅当：她当天所购数字的最小公倍数（LCM） 严格大于斯威珀当天所购数字的最小公倍数。

一组整数的最小公倍数（LCM）是指能被该组中所有整数整除的最小正整数。

然而，朵拉忘记了各 $a_i$ 的具体取值。请帮朵拉判断：是否存在一组正整数 $a_i$，使得她在每一天都战胜斯威珀？你无需具体求出这些 $a_i$ 的可能取值。

注意：在满足条件的一组解中，某些 $a_i$ 的值可以相等。

The first line contains integers $m$ and $n$ ($1\leq m \leq 50$, $1\leq n \leq 10^4$) — the number of days and the number of stores.

After this $m$ lines follow, the $i$-th line starts with an integer $s_i$ ($1\leq s_i \leq n-1$), the number of integers Dora bought on day $i$, followed by $s_i$ distinct integers, the indices of the stores where Dora bought an integer on the $i$-th day. The indices are between $1$ and $n$.

第一行包含两个整数 $m$ 和 $n$（$1\leq m \leq 50$，$1\leq n \leq 10^4$）——分别表示天数和商店数量。

接下来是 $m$ 行，其中第 $i$ 行首先是一个整数 $s_i$（$1\leq s_i \leq n-1$），表示 Dora 在第 $i$ 天购买的整数个数；随后是 $s_i$ 个互不相同的整数，表示 Dora 在第 $i$ 天购买整数的那些商店的编号。这些编号均在 $1$ 到 $n$ 之间。

Output must consist of a single line containing "possible" if there exist positive integers $a_i$ such that for each day the least common multiple of the integers bought by Dora is strictly greater than the least common multiple of the integers bought by Swiper on that day. Otherwise, print "impossible".

Note that you don't have to restore the integers themselves.

输出必须为单行，如果存在正整数 $a_i$，使得对每一天，Dora 所购整数的最小公倍数严格大于 Swiper 所购整数的最小公倍数，则输出 "possible"；否则输出 "impossible"。

注意：你无需恢复这些整数本身。

In the first sample, a possible choice for the values of the $a_i$ is $3, 4, 3, 5, 2$. On the first day, Dora buys the integers $3, 4$ and $3$, whose LCM is $12$, while Swiper buys integers $5$ and $2$, whose LCM is $10$. On the second day, Dora buys $3, 5$ and $2$, whose LCM is $30$, and Swiper buys integers $3$ and $4$, whose LCM is $12$.

在第一个样例中，$a_i$ 的一个可能取值为 $3, 4, 3, 5, 2$。第一天，Dora 购买了整数 $3, 4$ 和 $3$，它们的最小公倍数（LCM）为 $12$；而 Swiper 购买了整数 $5$ 和 $2$，它们的最小公倍数为 $10$。第二天，Dora 购买了 $3, 5$ 和 $2$，它们的最小公倍数为 $30$；Swiper 购买了整数 $3$ 和 $4$，它们的最小公倍数为 $12$。