## Bitwise Convolution 6

Points: 30 (partial)
Time limit: 1.0s
Memory limit: 512M

Authors:
Problem type
##### Bitwise Convolution Exercise 6
1. Exercise 1: Bitwise XOR convolution

2. Exercise 2: Bitwise OR convolution

3. Exercise 3: Bitwise AND convolution

4. Exercise 4: An operation that ORs the first bit, ANDs the second bit, and then repeats.

5. Exercise 5: An operation that ORs the first bit, ANDs the second bit, XORs the third one, and then repeats.

6. Exercise 6: XOR in base 3 (addition with no carry).

#### Input and Output Specification

The first line contains the integers ( ) and ( ), the exercise number and the length of the vectors and . The next line will contain and the line after will contain .

You will ouput the vector up until the last non-zero entry, where is the convolution operation of the respective subtask. Please output these numbers modulo .

#### Sample Input 1

6 3
1 2 3
1 1 2

#### Sample Output 1

8 9 7

#### Explanation

We are given that . Let denote the base-3 XOR (sum of digits in base 3 without carrying) operation. , so we add to . , so we add to .  , so we add to . #### Sample Input 2

6 4
1 2 2 2
1 1 2 3

#### Sample Output 2

7 7 6 5 8 10 6

#### Sample Input 3

6 2
0 0
0 0