A10462. Rebus

You are given a rebus of form ? + ? - ? + ? = n, consisting of only question marks, separated by arithmetic operation '+' and '-', equality and positive integer $n$ . The goal is to replace each question mark with some positive integer from $1$ to $n$ , such that equality holds.

The only line of the input contains a rebus. It's guaranteed that it contains no more than $100$ question marks, integer $n$ is positive and doesn't exceed $1000000$ , all letters and integers are separated by spaces, arithmetic operations are located only between question marks.

The first line of the output should contain "Possible" (without quotes) if rebus has a solution and "Impossible" (without quotes) otherwise.

If the answer exists, the second line should contain any valid rebus with question marks replaced by integers from $1$ to $n$ . Follow the format given in the samples.