Design Tutorial: Change the Goal

给定两个长为$n$的数组$x_i,y_i$。每次你可以选定$i,j$，令$x_i=x_i\ \mathbb{xor}\ x_j$（$i,j$可以相等）。要求若干次操作后使得$x$变成$y$，输出方案。 操作次数不能多于$10^6$，无解输出$-1$。 $n\leq10^4,\ 0\leq x_i,y_i\leq10^9$。

There are some tasks which have the following structure: you are given a model, and you can do some operations, you should use these operations to achive the goal. One way to create a new task is to use the same model and same operations, but change the goal. Let's have a try. I have created the following task for Topcoder SRM 557 Div1-Hard: you are given $ n $ integers $ x_{1},x_{2},...,x_{n} $ . You are allowed to perform the assignments (as many as you want) of the following form $ x_{i} $ ^= $ x_{j} $ (in the original task $ i $ and $ j $ must be different, but in this task we allow $ i $ to equal $ j $ ). The goal is to maximize the sum of all $ x_{i} $ . Now we just change the goal. You are also given $ n $ integers $ y_{1},y_{2},...,y_{n} $ . You should make $ x_{1},x_{2},...,x_{n} $ exactly equal to $ y_{1},y_{2},...,y_{n} $ . In other words, for each $ i $ number $ x_{i} $ should be equal to $ y_{i} $ .

There are some tasks which have the following structure: you are given a model, and you can do some operations, you should use these operations to achive the goal. One way to create a new task is to use the same model and same operations, but change the goal. Let's have a try. I have created the following task for Topcoder SRM 557 Div1-Hard: you are given $ n $ integers $ x_{1},x_{2},...,x_{n} $ . You are allowed to perform the assignments (as many as you want) of the following form $ x_{i} $ ^= $ x_{j} $ (in the original task $ i $ and $ j $ must be different, but in this task we allow $ i $ to equal $ j $ ). The goal is to maximize the sum of all $ x_{i} $ . Now we just change the goal. You are also given $ n $ integers $ y_{1},y_{2},...,y_{n} $ . You should make $ x_{1},x_{2},...,x_{n} $ exactly equal to $ y_{1},y_{2},...,y_{n} $ . In other words, for each $ i $ number $ x_{i} $ should be equal to $ y_{i} $ .

There are some tasks which have the following structure: you are given a model, and you can do some operations, you should use these operations to achive the goal. One way to create a new task is to use the same model and same operations, but change the goal. Let's have a try. I have created the following task for Topcoder SRM 557 Div1-Hard: you are given $ n $ integers $ x_{1},x_{2},...,x_{n} $ . You are allowed to perform the assignments (as many as you want) of the following form $ x_{i} $ ^= $ x_{j} $ (in the original task $ i $ and $ j $ must be different, but in this task we allow $ i $ to equal $ j $ ). The goal is to maximize the sum of all $ x_{i} $ . Now we just change the goal. You are also given $ n $ integers $ y_{1},y_{2},...,y_{n} $ . You should make $ x_{1},x_{2},...,x_{n} $ exactly equal to $ y_{1},y_{2},...,y_{n} $ . In other words, for each $ i $ number $ x_{i} $ should be equal to $ y_{i} $ .

2
3 5
6 0

2
1 2
2 2

5
0 0 0 0 0
1 2 3 4 5

-1

3
4 5 6
1 2 3

5
3 1
1 2
2 2
2 3
3 1

3
1 2 3
4 5 6

-1

Assignment $ a $ ^= $ b $ denotes assignment $ a $ = $ a $ ^ $ b $ , where operation "^" is bitwise XOR of two integers.