Polynomial Showdown

You are given the coefficients of a polynomial, listed from degree 8 down to degree 0 (the constant term). Print the polynomial in a clean, human-readable form with every unnecessary character removed.

For example, from the coefficients 0, 0, 0, 1, 22, -333, 0, 1, -1 you must print x^5 + 22x^4 - 333x^3 + x - 1.

The formatting rules are:

1. Terms appear in decreasing order of degree.
2. An exponent is written after a caret ^.
3. The constant term is written as the number alone.
4. Only terms with a nonzero coefficient are printed. If every coefficient is zero, print the single constant term 0.
5. The only spaces are a single space on each side of the binary + and - operators.
6. If the leading term is positive, no sign precedes it; a negative leading term is preceded by a minus sign, as in -7x^2 + 30x + 66.
7. A negated term is printed as the subtraction of its unnegated value (except for a negative leading term, which follows rule 6). So instead of x^2 + -3x, print x^2 - 3x.
8. The coefficients 1 and -1 are shown as a number only when they are the constant term. So instead of -1x^3 + 1x^2 + 3x^1 - 1, print -x^3 + x^2 + 3x - 1.

The input contains one or more lines. Each line holds nine coefficients separated by one or more spaces, listed from the degree-8 coefficient down to the degree-0 (constant) coefficient. Every coefficient is an integer whose absolute value is less than 1000.

For each input line, print the corresponding formatted polynomial on its own line, following the rules above.