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.

Input

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 1 000 000, all letters and integers are separated by spaces, arithmetic operations are located only between question marks.

Output

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.

Examples

Input

? + ? - ? + ? + ? = 42


Output

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


Input

? - ? = 1


Output

Impossible


Input

? = 1000000


Output

Possible
1000000 = 1000000
/* package whatever; // don't place package name! */

import java.util.*;
import java.lang.*;
import java.io.*;

public class equation
{
	private String equationInput;
	private int positiveDigitsCount;
	private int negativeDigitsCount;
	private int rightSideValue;
	
	private int minPositiveTotalValue;
	private int maxPositiveTotalValue;
	private int maxNegativeTotalValue;
	
	public static void main (String[] args) throws java.lang.Exception
	{
		Scanner sc = new Scanner(System.in);
		String input = sc.nextLine();
		
		equation objEquation= new equation();
		objEquation.parseEquationString(input);
		
		if( objEquation.isThereSolution() )
		{
			int[] totalSolution= objEquation.calculateTotalSolution();
			String resultText= objEquation.getResultText(totalSolution);
			
			System.out.println("Possible");
			System.out.println(resultText);
			
		}
		else
		{
			System.out.println("Impossible");
		}
	}
	
	private void parseEquationString( String equationInput  )
	{
		this.equationInput= equationInput.replace(" ", "");
		
		int equestionMarksCount= getCharacterCount( this.equationInput, '?' );
		
		this.negativeDigitsCount= getCharacterCount( this.equationInput, '-' );
		
		this.positiveDigitsCount= equestionMarksCount - negativeDigitsCount;
		
		int indexOfEqualCharacter= this.equationInput.indexOf('=');
		
		this.rightSideValue= Integer.parseInt( this.equationInput.substring( indexOfEqualCharacter + 1 ) );
	}
	
	private boolean isThereSolution( )
	{
		if ( this.positiveDigitsCount < 1   )
		{
			return false;
		} 
		
		minPositiveTotalValue= getMaxNumber( positiveDigitsCount, negativeDigitsCount + 1);
		maxPositiveTotalValue= rightSideValue * positiveDigitsCount;
		maxNegativeTotalValue= negativeDigitsCount * rightSideValue;

		
		if( maxPositiveTotalValue < minPositiveTotalValue || maxNegativeTotalValue < negativeDigitsCount )
		{
			return false;
		}
		else if(  (maxPositiveTotalValue - negativeDigitsCount) < rightSideValue )
		{
			return false;
		}
		else if( (minPositiveTotalValue - maxNegativeTotalValue) > rightSideValue )
		{
			return false;
		}
		
		return true;	
	}
	
	
	private int[] calculateTotalSolution()
	{
		int[] result= new int[2];
		
		int positiveTotalValueResult= maxPositiveTotalValue;
		int negativeTotalValueResult= negativeDigitsCount;
		
		int difference= positiveTotalValueResult - negativeTotalValueResult;
		
		//System.out.println("difference " + difference);
		
		
		if(  difference > rightSideValue )
		{
			positiveTotalValueResult -= (difference - rightSideValue);
			
			positiveTotalValueResult= getMaxNumber(positiveTotalValueResult, minPositiveTotalValue);
			
			difference= positiveTotalValueResult - negativeTotalValueResult;
			
			//System.out.println("difference " + difference);
		
			if( difference > rightSideValue )
			{
				negativeTotalValueResult += difference - rightSideValue;
			}
		}
/*
		System.out.println("positiveTotalValueResult " + positiveTotalValueResult);
		System.out.println("negativeTotalValueResult " + negativeTotalValueResult);
		*/ 
		result[0]= positiveTotalValueResult;
		result[1]= negativeTotalValueResult;
			
		return result;
		
	}
	
	private String getResultText(int[] totalSolution)
	{
		int totalPositiveSolution= totalSolution[0];
		int totalNegativeSolution= totalSolution[1];
		
		String resultText= equationInput;
		resultText= resultText.replace("-?", " - ?");
		resultText= resultText.replace("+?", " + ?");
		resultText= resultText.replace("=", " = ");

		if( negativeDigitsCount > 0 )
		{
			resultText= replaceEquationsWithNumbers( resultText, totalNegativeSolution, negativeDigitsCount, '-' );
		}
		
		resultText= replaceEquationsWithNumbers( resultText, totalPositiveSolution, positiveDigitsCount, '+' );
		
		return resultText;
	}
	
	private String replaceEquationsWithNumbers(String result, int totalValue, int marksCount, char signCharacter)
	{
		int markValue= totalValue / marksCount;
		int remainingeValue= totalValue % marksCount;
		
		for( int i=0; i < remainingeValue; i ++ )
		{
			result= result.replaceFirst("\\" + signCharacter + " \\?" , signCharacter + " " +  String.valueOf(1 +  markValue) );
		}
	
		result=  result.replace( signCharacter +  " ?",  signCharacter + " " + String.valueOf(markValue));
		
		
		if( signCharacter == '+' )
		{
			result= result.replaceFirst( "\\?",   String.valueOf(markValue));
		}
		
		return result;
	}
	
	
	private int getMaxNumber(int number1, int number2) 
	{
		if(number1 > number2){
			return number1;
		}
		else{
			return number2;
		}
	}
	
	
	private int getCharacterCount( String input, char searchCharacter )
	{
		return input.length() - input.replace( Character.toString(searchCharacter), "" ).length();
	} 
	
}
