Rebus

题意翻译

给你一个由问号、加、减、等于号构成的字符串和一个变量 $n$ 组成的等式。 大概长这样：`? + ? - ? = n `。 你现在要给每一个问号赋一个在 $1$ 到 $n$ 之间的值，使得该等式成立。 如果不可以的话输出一行一个字符串 `Impossible`。 否则输出两行，第一行一个字符串 `Possible`， 第二行输出该等式将问号都赋值之后的结果。

题目描述

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.

输入输出格式

输入格式

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.

输出格式

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.

输入输出样例

输入样例 #1

? + ? - ? + ? + ? = 42

输出样例 #1

Possible
9 + 13 - 39 + 28 + 31 = 42

输入样例 #2

? - ? = 1

输出样例 #2

Impossible

输入样例 #3

? = 1000000

输出样例 #3

Possible
1000000 = 1000000