Polynomial Showdown |

Given the coefficients of a polynomial from degree 8 down to 0, you
are to format the polynomial in a readable format with unnecessary
characters removed. For instance, given the coefficients 0, 0, 0, 1,
22, -333, 0, 1, and -1, you should generate an output line which
displays `x^5 + 22x^4 - 333x^3 + x - 1`

.

The formatting rules which must be adhered to are as follows:

- Terms must appear in decreasing order of degree.
- Exponents should appear after a caret ``
`^`

''. - The constant term appears as only the constant.
- Only terms with nonzero coefficients should appear, unless all terms have zero coefficients in which case the constant term should appear.
- The only spaces should be a single space on either side of the binary + and - operators.
- If the leading term is positive then no sign should precede it;
a negative leading term should be preceded by a minus sign, as in
`-7x^2 + 30x + 66`

. - Negated terms should appear as a subtracted unnegated term (with
the exception of a negative leading term which should appear as
described above). That is, rather than
`x^2 + -3x`

, the output should be`x^2 - 3x`

. - The constants 1 and -1 should appear only as the constant
term. That is, rather than
`-1x^3 + 1x^2 + 3x^1 - 1`

, the output should appear as`-x^3 + x^2 + 3x - 1`

.

The input file will contain one or more lines of coefficients delimited by one or more spaces. There are nine coefficients per line, each coefficient being an integer with a magnitude of less than 1000. The output file should contain the formatted polynomials, one per line.

0 0 0 1 22 -333 0 1 -1 0 0 0 0 0 0 -55 5 0

x^5 + 22x^4 - 333x^3 + x - 1 -55x^2 + 5x