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.

Sample Input 1

4 3
3 14 15 92
6 53 58

Sample Output 1

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).

Sample Input 2

4 4
1 2 3 4
100 200 300 400

Sample Output 2

1 2 3 4
5 6 7 8

Sample Input 3

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

Sample Output 3

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

见题面 Input 部分

见题面 Output 部分