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G. Mio and Lucky Array

time limit per test

5 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputMio 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

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

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.

Example

Input

5 5 1 2 3 4 5 5 2 0 6 0 10 5 1 2 3 4 5 3 3 5 3 8 -3 2 -3 -4 4 0 1 -2 4 10 -6 7 -7 5 1 2 3 4 5 4 1 10 1 1 5 0 0 0 0 0 2 10 12

Output

1 1 1 4 5 1 3 4 6 8 -1 -1

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.

Codeforces (c) Copyright 2010-2023 Mike Mirzayanov

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