Polynomial Multiplication 1

Standard input begins with an integer $T \le 100$, the number of test cases.

Each test case consists of two polynomials. A polynomial is given by an integer $1 \le n \le 255$ indicating the degree of the polynomial, followed by a sequence of integers $a_{0}, a_{1}, \ldots , a_{n}$, where $a_{i}$ is the coefficient of $x^{i}$ in the polynomial. All coefficients will fit in a signed 32-bit integer.

**NB!** The input and output files for
this problem are quite large, which means that you have to be a
bit careful about I/O efficiency.

For each test case, output the product of the two polynomials, in the same format as in the input (including the degree). All coefficients in the result will fit in a signed 32-bit integer.

Sample Input 1 | Sample Output 1 |
---|---|

2 2 1 0 5 1 0 -2 4 1 1 -1 1 1 4 9 -8 7 6 5 |
3 0 -2 0 -10 8 9 1 -10 30 5 -2 8 11 5 |