Math Tutoring

You are teaching a friend the rule for differentiating a polynomial, and no matter how many examples you work through, the rule does not stick. So you decide to write a program that computes the derivative for him.

Differentiating the polynomial

$a_n x^n + a_{n-1} x^{n-1} + \dots + a_2 x^2 + a_1 x + a_0$

gives

$n a_n x^{n-1} + (n-1) a_{n-1} x^{n-2} + \dots + 2 a_2 x + a_1$

For example, the derivative of $2x^3 - x + 3$ is $6x^2 - 1$, and the derivative of $3x^4 + 2x^3 + 7x^2 + 5x + 7$ is $12x^3 + 6x^2 + 14x + 5$.

Given a polynomial, print its derivative. Only polynomials of the form shown above appear in this problem.

The first line contains the number of test cases.

Each test case is given on a single line. The first integer on the line is the highest exponent $n$ ($1 \le n \le 100$) of the polynomial, followed by $n+1$ coefficients, one for each term from $x^n$ down to $x^0$. Every coefficient is an integer between $-1000$ and $1000$, inclusive. The highest exponent is always positive. All numbers are separated by a single space.

Print one line for each test case. The line starts with Case x:, where $x$ is the test case number counting from 1. Put a single space after the colon and then write the derivative.

Write the derivative in the same format as the input. The first value is the highest exponent $n-1$ of the derivative, followed by its $n$ coefficients from $x^{n-1}$ down to $x^0$. Separate the values with a single space, and print the leading coefficient even when it is 0.