Problem Statement

You are given a string $s=s_1s_2\dots s_N$ of length $N$ consisting of a,b, and positive integers $A,B$.

Does there exist a pair of integer sequences of length $N$, $a=(a_1,a_2,\dots,a_N),b=(b_1,b_2,\dots,b_N)$, satisfying all of the following conditions?

• Among the $2N$ integers $a_1,a_2,\dots,a_N,b_1,b_2,\dots,b_N$, each integer between $1$ and $2N$, inclusive, appears exactly $1$ time.
• The length of the longest increasing subsequence of the integer sequence $a=(a_1,a_2,\dots,a_N)$ is $A$.
• The length of the longest increasing subsequence of the integer sequence $b=(b_1,b_2,\dots,b_N)$ is $B$.
• For each $i=1,2,\dots,N$, if $s_i=$ a then $a_i > b_i$, and if $s_i=$ b then $a_i < b_i$.

If such a pair exists, show one such pair of integer sequences $a,b$.

For each input, answer $T$ test cases.

Constraints

• $1 \le T \le 2 \times 10^4$
• $1 \le N \le 2 \times 10^5$
• $1 \le A,B \le N$
• $T,N,A,B$ are integers.
• $s$ is a string of length $N$ consisting of a,b.
• The sum of $N$ over the $T$ test cases in a single input is at most $2\times10^5$.

Input

First, line $1$ contains the number of test cases $T$ in the input.

$T$

Then, $T$ test cases follow over $2T$ lines. Each test case is given over $2$ lines in the following format.

$N\ \ A\ \ B$
$s$

Output

Output the answers to the test cases in order as follows, with a line break after each test case.

• If no pair of integer sequences $a,b$ satisfying the conditions exists, output No.
• If one exists, output Yes and $a,b$ in the following format (if multiple pairs $a,b$ satisfy the conditions, you may output any of them).

  Yes
  $a_1\ \ a_2\ \ \cdots\ \ a_N$
  $b_1\ \ b_2\ \ \cdots\ \ b_N$

Sample

3
4 3 2
bbaa
2 2 1
ab
5 5 5
bbbbb

Yes
1 7 5 6
3 8 4 2
No
Yes
1 2 3 4 5
6 7 8 9 10