Fence Painting

Problem Description

There are $n$ fence planks numbered from $1$. The $i$-th plank currently has colour $a_i$, and you want to repaint the $i$-th plank to colour $b_i$.

There are $m$ painters who will work in turn. The $j$-th painter will paint one plank with colour $c_j$. You may decide which plank each painter paints, but you cannot leave a painter idle.

Determine whether all planks can be repainted to their target colours; if so, output a plan.

Input Format

Multiple test cases.

The first line contains an integer $T$ ($1 \le T \le 10000$).

For each test case, the first line contains two integers $n, m$ ($1 \le n, m \le 100000$) separated by a space.

The next line contains $n$ integers $a_i$ ($1 \le a_i \le n$).

The next line contains $n$ integers $b_i$ ($1 \le b_i \le n$).

The next line contains $m$ integers $c_i$ ($1 \le c_i \le n$).

It is guaranteed that $\sum n, \sum m \le 100000$.

Output Format

For each test case, if the planks cannot be repainted to the target colours, output one line containing NO.

If they can, first output one line containing YES.

Then output one line with $m$ integers, indicating which plank (by number) the $j$-th arriving painter should paint. There may be multiple valid plans; output any of them.

Sample Input

6
1 1
1
1
1
5 2
1 2 2 1 1
1 2 2 1 1
1 2
3 3
2 2 2
2 2 2
2 3 2
10 5
7 3 2 1 7 9 4 2 7 9
9 9 2 1 4 9 4 2 3 9
9 9 7 4 3
5 2
1 2 2 1 1
1 2 2 1 1
3 3
6 4
3 4 2 4 1 2
2 3 1 3 1 1
2 2 3 4

Sample Output

YES
1
YES
2 2
YES
1 1 1
YES
2 1 9 5 9
NO
NO