Problem Statement

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.

Notes

• In each output, insert a newline at the end and flush Standard Output. Otherwise, the verdict may be TLE