Deja Vu

题意翻译

给定一个有向图，无重边或自环。 每条边上给定一个顶点序列。将一条路径上的边的顶点序列依次连接起来，组成一个新的顶点序列A，将路径上的点依次连接起来，组成一个顶点序列$B$，如果$A$与$B$相同，则该路径令人震惊。 [子问题$E1$](https://codeforces.com/problemset/problem/331/E1)：输出任意一条长度在$[1,2n]$之间的令人震惊的路径，不存在则输出$0$。 [子问题$E2$](https://codeforces.com/problemset/problem/331/E2)：求出长度为$i(1 \leq i \leq n)$的令人震惊的路径的数量（模$10^9+7$）。

题目描述

Everybody knows that we have been living in the Matrix for a long time. And in the new seventh Matrix the world is ruled by beavers. So let's take beaver Neo. Neo has so-called "deja vu" outbursts when he gets visions of events in some places he's been at or is going to be at. Let's examine the phenomenon in more detail. We can say that Neo's city is represented by a directed graph, consisting of $ n $ shops and $ m $ streets that connect the shops. No two streets connect the same pair of shops (besides, there can't be one street from A to B and one street from B to A). No street connects a shop with itself. As Neo passes some streets, he gets visions. No matter how many times he passes street $ k $ , every time he will get the same visions in the same order. A vision is a sequence of shops. We know that Neo is going to get really shocked if he passes the way from some shop $ a $ to some shop $ b $ , possible coinciding with $ a $ , such that the list of visited shops in the real life and in the visions coincide. Suggest beaver Neo such path of non-zero length. Or maybe you can even count the number of such paths modulo $ 1000000007 $ $ (10^{9}+7) $ ?..

输入输出格式

输入格式

The first line contains integers $ n $ and $ m $ — the number of shops and the number of streets, correspondingly, $ 1<=n<=50 $ , . Next $ m $ lines contain the descriptions of the streets in the following format: $ x_{i} $ $ y_{i} $ $ k_{i} $ $ v_{1} $ $ v_{2} $ ... $ v_{k} $ , where $ x_{i} $ and $ y_{i} $ $ (1<=x_{i},y_{i}<=n,x_{i}≠y_{i}) $ are indices of shops connected by a street, $ k_{i} $ $ (0<=k_{i}<=n) $ is the number of visions on the way from $ x_{i} $ to $ y_{i} $ ; $ v_{1} $ , $ v_{2} $ , ..., $ v_{k} $ $ (1<=v_{i}<=n) $ describe the visions: the numbers of the shops Neo saw. Note that the order of the visions matters. It is guaranteed that the total number of visions on all streets doesn't exceed $ 10^{5} $ . - to get 50 points, you need to find any (not necessarily simple) path of length at most $ 2·n $ , that meets the attributes described above (subproblem E1); - to get 50 more points, you need to count for each length from $ 1 $ to $ 2·n $ the number of paths that have the attribute described above (subproblem E2).

输出格式

Subproblem E1. In the first line print an integer $ k $ $ (1<=k<=2·n) $ — the numbers of shops on Neo's path. In the next line print $ k $ integers — the number of shops in the order Neo passes them. If the graph doesn't have such paths or the length of the shortest path includes more than $ 2·n $ shops, print on a single line $ 0 $ . Subproblem E2. Print $ 2·n $ lines. The $ i $ -th line must contain a single integer — the number of required paths of length $ i $ modulo $ 1000000007 $ $ (10^{9}+7) $ .

输入输出样例

输入样例 #1

6 6
1 2 2 1 2
2 3 1 3
3 4 2 4 5
4 5 0
5 3 1 3
6 1 1 6

输出样例 #1

4
6 1 2 3

输入样例 #2

6 6
1 2 2 1 2
2 3 1 3
3 4 2 4 5
4 5 0
5 3 1 3
6 1 1 6

输出样例 #2

1
2
1
1
2
1
1
2
1
1
2
1

说明

The input in both samples are the same. The first sample contains the answer to the first subproblem, the second sample contains the answer to the second subproblem.

题意翻译

给定一个有向图，无重边或自环。 每条边上给定一个顶点序列。将一条路径上的边的顶点序列依次连接起来，组成一个新的顶点序列A，将路径上的点依次连接起来，组成一个顶点序列$B$，如果$A$与$B$相同，则该路径令人震惊。 [子问题$E1$](https://codeforces.com/problemset/problem/331/E1)：输出任意一条长度在$[1,2n]$之间的令人震惊的路径，不存在则输出$0$。 [子问题$E2$](https://codeforces.com/problemset/problem/331/E2)：求出长度为$i(1 \leq i \leq n)$的令人震惊的路径的数量（模$10^9+7$）。