### Problem Statement

You are given strictly increasing sequences of length $N$ and $M$: $A=(A _ 1,A _ 2,\ldots,A _ N)$ and $B=(B _ 1,B _ 2,\ldots,B _ M)$. Here, $A _ i\neq B _ j$ for every $i$ and $j$ $(1\leq i\leq N,1\leq j\leq M)$.

Let $C=(C _ 1,C _ 2,\ldots,C _ {N+M})$ be a strictly increasing sequence of length $N+M$ that results from the following procedure.

-   Let $C$ be the concatenation of $A$ and $B$. Formally, let $C _ i=A _ i$ for $i=1,2,\ldots,N$, and $C _ i=B _ {i-N}$ for $i=N+1,N+2,\ldots,N+M$.
-   Sort $C$ in ascending order.

For each of $A _ 1,A _ 2,\ldots,A _ N, B _ 1,B _ 2,\ldots,B _ M$, find its position in $C$. More formally, for each $i=1,2,\ldots,N$, find $k$ such that $C _ k=A _ i$, and for each $j=1,2,\ldots,M$, find $k$ such that $C _ k=B _ j$.

### Input

The input is given from Standard Input in the following format:

```
$N$ $M$
$A _ 1$ $A _ 2$ $\ldots$ $A _ N$
$B _ 1$ $B _ 2$ $\ldots$ $B _ M$
```

### Output

Print the answer in two lines.  
The first line should contain the positions of $A _ 1,A _ 2,\ldots,A _ N$ in $C$, with spaces in between.  
The second line should contain the positions of $B _ 1,B _ 2,\ldots,B _ M$ in $C$, with spaces in between.

### Constraints

-   $1\leq N,M\leq 10^5$
-   $1\leq A _ 1\lt A _ 2\lt\cdots\lt A _ N\leq 10^9$
-   $1\leq B _ 1\lt B _ 2\lt\cdots\lt B _ M\leq 10^9$
-   $A _ i\neq B _ j$ for every $i$ and $j$ $(1\leq i\leq N,1\leq j\leq M)$.
-   All values in the input are integers.

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