Switch Grid

There is a grid with N rows and M columns. The rows are numbered from 0 to N − 1 and columns are numbered from 0 to M − 1. Each of the cell in row 0 and each of the cell in column 0 contains a bulb. Except the cell in row 0 and column 0 is empty. All the other rows can contain a switch. The switch in the cell on row r and column c change the states of both bulbs in row r and column c. You are given the initial states and the desired states of each of the bulb. Now given a list of switches you need to press them in such a way that all the bulbs change their states from their initial to desired states. Input Input contains multiple test cases. First line contains T the number of test cases. Each of the test case consists of 7 lines.

1. 3 space separated integers N (1 ≤ N ≤ 1000),M (1 ≤ M ≤ 1000) and S (1 ≤ S ≤ 4000). N is the number of rows in the grid, M is the number of columns in the grid and S is the number of switches.
2. N − 1 space separated integers. Each of these integers is either ‘0’ or ‘1’. The i-th (i starts from 1) denotes the initial state of the bulb in (i, 0). 0 means off and 1 means on.
3. N − 1 space separated integers. Each of these integers is either ‘0’ or ‘1’. The i-th (i starts from 1) denotes the final state of the bulb in (i, 0).
4. M − 1 space separated integers. Each of these integers is either ‘0’ or ‘1’. The i-th (i starts from 1) denotes the initial state of the bulb in (0, i).
5. M − 1 space separated integers. Each of these integers is either ‘0’ or ‘1’. The i-th (i starts from 1) denotes the final state of the bulb in (0, i).
6. S space separated integers. Each of these integers is between 1 and N − 1 inclusive. The i-th (i starts from 0) integers denote the row number of the i-th switch.
7. S space separated integers. Each of these integers is between 1 and M − 1 inclusive. The i-th (i starts from 0) integers denote the column number of the i-th switch. There is a blank line after each of the test case. There will be 100 test cases. Output For each test case output contains a single line. When there is no way to transform the state of all the bulbs the line contains ‘-1’. Otherwise the line starts with X followed by X integers. X is the number of switch presses required to transform all the bulbs into the desired states. X should be less than 10000. The next X integers denotes the indices of the switches that need to be pressed. All of these X integers should be distinct. Any combination of switch presses that transforms all the bulbs to their desired state will be considered correct.

2/2 Sample Input 3 332 00 10 00 01 12 12 333 00 11 00 11 112 122 445 000 011 000 101 11223 13122 Sample Output -1 202 40134