## Bitwise Convolution 1, 2, 3

Points: 20 (partial)
Time limit: 1.0s
Memory limit: 512M

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Problem type
##### Bitwise Convolution Exercises 1, 2, 3

This is a practice problem for bitwise convolution using the Fast Walsh–Hadamard transform. Exercises come from here.

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 a vector of length , the vector , where is the convolution operation of the respective subtask. Please output these numbers modulo .

#### Sample Input 1

1 2
1 2
3 4

#### Sample Output 1

11 10 0 0

#### Explanation

We are given that . , so let denote the bitwise XOR operation.

#### Sample Input 2

3 2
1 2
3 4

#### Sample Output 2

13 8 0 0

#### Explanation

We are given that . , so let denote the bitwise AND operation.