Description:
Mio has an array $$$a$$$ consisting of $$$n$$$ integers, and an array $$$b$$$ consisting of $$$m$$$ integers.
Mio can do the following operation to $$$a$$$:
- Choose an integer $$$i$$$ ($$$1 \leq i \leq n$$$) that has not been chosen before, then add $$$1$$$ to $$$a_i$$$, subtract $$$2$$$ from $$$a_{i+1}$$$, add $$$3$$$ to $$$a_{i+2}$$$ an so on. Formally, the operation is to add $$$(-1)^{j-i} \cdot (j-i+1) $$$ to $$$a_j$$$ for $$$i \leq j \leq n$$$.
Mio wants to transform $$$a$$$ so that it will contain $$$b$$$ as a subarray. Could you answer her question, and provide a sequence of operations to do so, if it is possible?
An array $$$b$$$ is a subarray of an array $$$a$$$ if $$$b$$$ can be obtained from $$$a$$$ by deletion of several (possibly, zero or all) elements from the beginning and several (possibly, zero or all) elements from the end.
Input Format:
The input consists of multiple test cases. The first line contains a single integer $$$t$$$ ($$$1 \leq t \leq 10^4$$$) — the number of test cases. The description of test cases follows.
The first line of each test case contains one integer $$$n$$$ ($$$2 \leq n \leq 2 \cdot 10^5$$$) — the number of elements in $$$a$$$.
The second line of the test case contains $$$n$$$ integers $$$a_1, a_2, \cdots, a_n$$$ ($$$-10^5 \leq a_i \leq 10^5$$$), where $$$a_i$$$ is the $$$i$$$-th element of $$$a$$$.
The third line of the test case contains one integer $$$m$$$ ($$$2 \leq m \leq n$$$) — the number of elements in $$$b$$$.
The fourth line of the test case contains $$$m$$$ integers $$$b_1, b_2, \cdots, b_m$$$ ($$$-10^{12} \leq b_i \leq 10^{12}$$$), where $$$b_i$$$ is the $$$i$$$-th element of $$$b$$$.
It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2 \cdot 10^5$$$.
Output Format:
If it is impossible to transform $$$a$$$ so that it contains $$$b$$$ as a subarray, output $$$-1$$$.
Otherwise, the first line of output should contain an integer $$$k$$$ ($$$0 \leq k \leq n$$$), the number of operations to be done.
The second line should contain $$$k$$$ distinct integers, representing the operations done in order.
If there are multiple solutions, you can output any.
Notice that you do not need to minimize the number of operations.
Note:
In the first test case, the sequence $$$a$$$ = $$$[1,2,3,4,5]$$$. One of the possible solutions is doing one operation at $$$i = 1$$$ (add $$$1$$$ to $$$a_1$$$, subtract $$$2$$$ from $$$a_2$$$, add $$$3$$$ to $$$a_3$$$, subtract $$$4$$$ from $$$a_4$$$, add $$$5$$$ to $$$a_5$$$). Then array $$$a$$$ is transformed to $$$a$$$ = $$$[2,0,6,0,10]$$$, which contains $$$b$$$ = $$$[2, 0, 6, 0, 10]$$$ as a subarray.
In the second test case, the sequence $$$a$$$ = $$$[1,2,3,4,5]$$$. One of the possible solutions is doing one operation at $$$i = 4$$$ (add $$$1$$$ to $$$a_4$$$, subtract $$$2$$$ from $$$a_5$$$). Then array $$$a$$$ is transformed to $$$a$$$ = $$$[1,2,3,5,3]$$$, which contains $$$b$$$ = $$$[3,5,3]$$$ as a subarray.
In the third test case, the sequence $$$a$$$ = $$$[-3, 2, -3, -4, 4, 0, 1, -2]$$$. One of the possible solutions is the following.
- Choose an integer $$$i=8$$$ to do the operation. Then array $$$a$$$ is transformed to $$$a$$$ = $$$[-3, 2, -3, -4, 4, 0, 1, -1]$$$.
- Choose an integer $$$i=6$$$ to do the operation. Then array $$$a$$$ is transformed to $$$a$$$ = $$$[-3, 2, -3, -4, 4, 1, -1, 2]$$$.
- Choose an integer $$$i=4$$$ to do the operation. Then array $$$a$$$ is transformed to $$$a$$$ = $$$[-3, 2, -3, -3, 2, 4, -5, 7]$$$.
- Choose an integer $$$i=3$$$ to do the operation. Then array $$$a$$$ is transformed to $$$a$$$ = $$$[-3, 2, -2, -5, 5, 0, 0, 1]$$$.
- Choose an integer $$$i=1$$$ to do the operation. Then array $$$a$$$ is transformed to $$$a$$$ = $$$[-2, 0, 1, -9, 10, -6, 7, -7]$$$.
The resulting $$$a$$$ is $$$[-2, 0, 1, -9, 10, -6, 7, -7]$$$, which contains $$$b$$$ = $$$[10, -6, 7, -7]$$$ as a subarray.
In the fourth test case, it is impossible to transform $$$a$$$ so that it contains $$$b$$$ as a subarray.
In the fifth test case, it is impossible to transform $$$a$$$ so that it contains $$$b$$$ as a subarray.