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문제

There are $n+m$ towns in Kingdom of Coffee Chicken, which can be seen as $n+m$ integers coordinates $(x_i,y_i)$ on the 2-dimensional plane. $n$ of them belong to Acesrc while the other $m$ towns belong to Roundgod.

Now both Acesrc and Roundgod want to build straight roads among their towns and they all want their towns are connected, which means there is a path between any two of towns. It is obvious that we need only $n+m-2$ roads to make it possible. Moreover, Acesrc and Roundgod hope that among these $n+m-2$ roads, there is no intersection other than the position of towns.

Now we hope you to provide us a construction plan.

입력

The first line contains two integers $n,m(n>1,m>1,n+m \leq 3000)$.

The following $n$ lines describe Acesrc's towns and each line contains two integers $x,y(0 \leq x,y \leq 10^9)$ representing coordinates. Their number is $1-n$ respectively.

The following $n$ lines describe Roundgod's towns and each line contains two integers $x,y(0 \leq x,y \leq 10^9)$ representing coordinates. Their number is $1-m$ respectively.

There is no repeated coordinates among those $n+m$ towns. We also guarantee that no three towns are on the same straight line among them.

출력

Please output $n+m-2$ lines in total, the first $n-1$ lines representing the construction plan of Acesrc's towns and the other $m-1$ lines representing the construction plan of Roundgod's towns. For each line of a construction plan, please output two integers $x,y$, indicating a straight road connected town $x$ and $y$. 

If it is impossible to find any valid construction plan, output Impossible instead.

예제 입력 1

2 3
0 0
1 1
1 0
0 1
2 3

예제 출력 1

2 1
1 3
3 2