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C - Merge Sequences

Score : $300$ points

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 $C _ k=B _ j$.

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.

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.

4 3
3 14 15 92
6 53 58

1 3 4 7
2 5 6

$C$ will be $(3,6,14,15,53,58,92)$. Here, the $1$-st, $3$-rd, $4$-th, $7$-th elements are from $A=(3,14,15,92)$, and the $2$-nd, $5$-th, $6$-th elements are from $B=(6,53,58)$.

4 4
1 2 3 4
100 200 300 400

1 2 3 4
5 6 7 8

8 12
3 4 10 15 17 18 22 30
5 7 11 13 14 16 19 21 23 24 27 28

1 2 5 9 11 12 15 20
3 4 6 7 8 10 13 14 16 17 18 19