This is an **interactive problem** (where your program and the judge program interact through Standard Input and Output).
There is a simple connected undirected graph with $N$ vertices and $M$ edges. The vertices are numbered with integers from $1$ to $N$.
Initially, you are at vertex $1$. Repeat moving to an adjacent vertex at most $2N$ times to reach vertex $N$.
Here, you do not initially know all edges of the graph, but you will be informed of the vertices adjacent to the vertex you are at.
## Constraints
* $2\leq N\leq100$
* $N-1\leq M\leq\dfrac{N(N-1)}2$
* The graph is simple and connected.
* All input values are integers.
## Input And Output
First, receive the number of vertices $N$ and the number of edges $M$ in the graph from Standard Input:
$N$ $M$
Next, you get to repeat the operation described in the problem statement at most $2N$ times against the judge.
At the beginning of each operation, the vertices adjacent to the vertex you are currently at are given from Standard Input in the following format:
$k$ $v _ 1$ $v _ 2$ $\ldots$ $v _ k$
Here, $v _ i\ (1\leq i\leq k)$ are integers between $1$ and $N$ such that $v _ 1\lt v _ 2\lt\cdots\lt v _ k$.
Choose one of $v _ i\ (1\leq i\leq k)$ and print it to Standard Output in the following format:
$v _ i$
After this operation, you will be at vertex $v _ i$.
If you perform more than $2N$ operations or print invalid output, the judge will send `-1` to Standard Input.
If the destination of a move is vertex $N$, the judge will send `OK` to Standard Input and terminate.
When receiving `-1` or `OK`, immediately terminate the program.
[samples]
## Notes
* **In each output, insert a newline at the end and flush Standard Output. Otherwise, the verdict may be TLE.**
* **The verdict will be indeterminate if the program prints invalid output or quits prematurely in the middle of the interaction.**
* Terminate the program immediately after reaching vertex $N$. Otherwise, the verdict will be indeterminate.
* **The judge for this problem is adaptive. This means that the graph may change without contradicting the constraints or previous outputs.**