Plotting Polynomials

A graphing calculator draws a function on screen with almost no work from the student. The processor in such a calculator is slow, so the drawing routine has to be economical. This problem asks you to implement a method that speeds up the plotting of a polynomial.

Given a polynomial $p(x) = a_n x^n + \dots + a_1 x + a_0$ of degree $n$, you want to plot it at the $m$ integer points $x = 0, 1, \dots, m-1$. Evaluating the polynomial directly at each point costs $mn$ multiplications and $mn$ additions.

Reusing earlier results cuts that cost. If $p(x) = a_1 x + a_0$ and $p(i)$ is already known, then $p(i+1) = p(i) + a_1$, so every later value costs one addition.

In general, once the initialization is done, $n$ additions turn $p(i)$ into $p(i+1)$. With the constants $C_0, C_1, \dots, C_n$ chosen correctly, the pseudocode below produces $p(i)$.

p(0) = C_0; t_1 = C_1; ... t_n = C_n;
for i from 1 to m-1 do
     p(i)    = p(i-1)  + t_1;
     t_1     = t_1     + t_2;
     t_2     = t_2     + t_3;
              :
              :
     t_(n-1) = t_(n-1) + t_n;
end

For $p(x) = a_1 x + a_0$ you can take $C_0 = a_0$ and $C_1 = a_1$.

Compute the constants $C_0, C_1, \dots, C_n$ that make the pseudocode give the correct value of $p(i)$ for every $i = 0, \dots, m-1$.

The input is a single line. The first integer is $n$, with $1 \le n \le 6$. It is followed by the $n+1$ integer coefficients $a_n, \dots, a_1, a_0$. Every coefficient satisfies $|a_i| \le 50$, and $a_n \neq 0$.

Print $C_0, C_1, \dots, C_n$ on one line, separated by single spaces.