Grammy has a connected undirected graph  with two special vertices  and . Each of the vertices has a number  written on it, where  is a permutation of size . 

Grammy thinks these numbers on vertices are too chaotic. She wants to reorder the numbers such that for each vertex , there exists a path satisfying the following conditions: 

1. The path starts from  and ends at . 

2. The path contains vertex . 

3. The numbers along the path are strictly increasing. 

Sadly, in each operation, Grammy can only choose a simple path starting from  and ending at an arbitrary vertex, then shift the numbers on the simple path by 1. That is, if the vertices on the simple path chosen by Grammy contains , then after Grammy's operation, these vertices will become . 

Additionally, Grammy can only operate no more than  times. 

Grammy cannot find out any plan to solve this problem, so she asked you for help. 

Please help Grammy to determine whether she can reorder the numbers. You also need to output a solution if it exists. 

The first line contains  integers  (). 

The second line contains  integers  (). It is guaranteed that  is a permutation. 

In each of the next  lines, there are two integers  (), denoting that there is a bidirectional edge between  and . It is guaranteed that the graph is connected. 

If Grammy cannot properly reorder the numbers, output  (without quotes). 

Otherwise output an integer  () in the first line, indicating the number of operations Grammy needs. 

For the following  lines, output an integer , denoting the number of vertices on the chosen simple path. Then output  integers (), indicating the vertices on the simple path. These  should be distinct. 

It can be proved that if graph  can be properly reordered, there exists a solution with no more than  operations. 

Note that you don't have to minimize . If there are multiple solutions, output any of them. 

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

7
4 1 3 2 4
3 1 3 2
3 1 3 5
4 1 3 2 4
3 1 3 2
2 1 3
1 1

4 3 1 2
1 4 2 3
1 4
2 4
3 4

-1