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
import java.io.*;
import java.util.*;
import java.util.Map.Entry;


public class Task_Rnd664_B {

	final static String input_file_name = "input/Rnd664_B.txt";
	
	public static void main(String[] args)
	{
		//!!!!!!!!!!111
		reader.init(true);		//to server
		//reader.init(false);
		
		run();
		wr.flush();
	}

    public static void run()
    {
    	String s = reader.readln();
    	
    	int xx = 0;
    	int kk = 0;
    	int nn = 0;
    	boolean plus = true;
    	for (int ii = 0; ii < s.length(); ii++)
    	{
    		char cc = s.charAt(ii);
    		if (cc == '+')
    			plus = true;
    		if (cc == '-')
    			plus = false;
    		if (cc == '?')
    		{
    			if (plus)
    				xx++;
    			else
    				kk++;
    		}
    		if (cc == '=')
    		{
    			String s2 = s.substring(ii+1, s.length());
    			s2 = s2.trim();
    			nn = Integer.valueOf(s2);
    			break;
    		}
    	}
    	
    	if (xx*nn - kk * 1 < nn || xx * 1 - kk * nn > nn)
    	{
        	wr.print("Impossible");
    		wr2.endl();
    		return;
    	}
    	
    	int vv = xx * nn - kk * 1;
    	int ll = vv - nn;
    	
    	int aa1[] = new int[xx];
    	int aa2[] = new int[kk+1];
    	
    	for (int ii = 0; ii < xx; ii++)
    		aa1[ii] = nn;

    	for (int ii = 0; ii < kk; ii++)
    		aa2[ii] = 1;
    	
    	int ii = 0;
    	while (ll > 0 && ii < xx)
    	{
    		int bb = aa1[ii]-1;
    		if (bb > ll)
    			bb = ll;
    		aa1[ii] -= bb;
    		ll -= bb;
    		ii++;
    	}

    	ii = 0;
    	while (ll > 0 && ii < kk)
    	{
    		int bb = nn-aa2[ii];
    		if (bb > ll)
    			bb = ll;
    		aa2[ii] += bb;
    		ll -= bb;
    		ii++;
    	}
    	
    	if (ll > 0)
    	{
        	wr.print("Impossible");
    		wr2.endl();
    		return;
    	}

    	wr.print("Possible");
    	wr2.endl();
    	int ind1 = 0;
    	int ind2 = 0;
    	plus = true;
    	for (int jj = 0; jj < s.length(); jj++)
    	{
    		char cc = s.charAt(jj);
    		if (cc == '+')
    		{
    			plus = true;
    			wr.print("+ ");
    		}
    		if (cc == '-')
    		{
    			plus = false;
    			wr.print("- ");
    		}
    		if (cc == '?')
    		{
    			if (plus)
    			{
    				wr.print(aa1[ind1++]);
    				wr.print(" ");
    			}
    			else
    			{
    				wr.print(aa2[ind2++]);
    				wr.print(" ");
    			}
    		}
    		if (cc == '=')
    		{
    			String s2 = s.substring(jj, s.length());
    			wr.print(s2);
    			break;
    		}
    	}
    	
    	
		wr2.endl();
    }
	
     
    static public PrintWriter wr; 
    static OutputWriter wr2=new OutputWriter(System.out);
	static class reader{
		static BufferedReader br; static StringTokenizer tkn;
		static String readln() { try { return br.readLine(); } catch (Exception e) { return ""; } }
		static void init(boolean console) {
			if (console) { br=new BufferedReader(new InputStreamReader(System.in)); }
			else { try { br=new BufferedReader(new InputStreamReader(new FileInputStream(input_file_name))); }
				catch (Exception e) { System.exit(551); } }
			tkn=new StringTokenizer("");
		}
		static String next() { while (!tkn.hasMoreTokens()){ tkn=new StringTokenizer(readln()); } return tkn.nextToken(); }
		static int nextInt(){ while (!tkn.hasMoreTokens()){ tkn=new StringTokenizer(readln()); } return Integer.parseInt(tkn.nextToken()); }
		static long nextLong(){ while (!tkn.hasMoreTokens()){ tkn=new StringTokenizer(readln()); } return Long.parseLong(tkn.nextToken()); }
		static double nextDouble(){ while (!tkn.hasMoreTokens()){ tkn=new StringTokenizer(readln()); } return Double.parseDouble(tkn.nextToken()); }
	}
    static class OutputWriter {
        OutputWriter(OutputStream stream) { wr = new PrintWriter(stream); }
        public void printf(String format, Object... args) { wr.print(String.format(Locale.ENGLISH, format, args)); }
        public void endl() { wr.print("\n"); }
    }
}
