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.BufferedReader;
import java.io.FileNotFoundException;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.StringTokenizer;


 
 
public class Main
{
    static StringTokenizer st;//=new StringTokenizer("");
    static BufferedReader br;
    
    ///////////////////////////////////////////////////////////////////////////////////
    public static void main(String args[]) throws FileNotFoundException, IOException, Exception
    {
        //Scanner in =new Scanner(new FileReader("input.txt"));
        //PrintWriter out = new PrintWriter(new FileWriter("output.txt"));
        //Scanner in=new Scanner(System.in);
        br=new BufferedReader(new InputStreamReader(System.in));
        PrintWriter out=new PrintWriter(System.out);
        //StringTokenizer st;//=new StringTokenizer(br.readLine());
        //////////////////////////////////////////////////////////////////////////////////////
        
        int p=0;
        int m=0;
        boolean pos=true;
        boolean neg=false;
        int n=0;
        String s[]=br.readLine().split(" ");
        for(int i=0;i<s.length;i++)
        {
            if(s[i].charAt(0)=='?')
            {
                if(pos) p++;
                else m++;
            }
            else if(s[i].charAt(0)=='+')
            {
                pos=true;
                neg=false;
            }
            else if(s[i].charAt(0)=='-')
            {
                pos=false;
                neg=true;
            }
            else if(s[i].charAt(0)=='=')
            {
                i++;
                n=Integer.parseInt(s[i]);
                break;
            }
        }
        if(p*n-m<n || p-n*m>n)
        {
            out.print("Impossible");
            out.close();
            return ;
        }
        else
        {
            out.println("Possible");
            int po[]=new int[p];
            int ne[]=new int[m];
            if(p-m==n)
            {
                for(int i=0;i<p;i++) po[i]=1;
                for(int i=0;i<m;i++) ne[i]=1;
            }
            else if(p-m<n)
            {
                for(int i=0;i<m;i++) ne[i]=1;
                for(int i=0;i<(n-(p-m))%p;i++) po[i]=1;
                for(int i=0;i<p;i++) po[i]+=(n-(p-m))/p+1;
            }
            else
            {
                for(int i=0;i<p;i++) po[i]=1;
                for(int i=0;i<((p-m)-n)%m;i++) ne[i]=1;
                for(int i=0;i<m;i++) ne[i]+=((p-m)-n)/m+1;
            }
            pos=true;
            neg=false;
            int p1=0;
            int n1=0;
            for(int i=0;i<s.length;i++)
            {
                if(s[i].charAt(0)=='?')
                {
                    if(pos) out.print(po[p1++]+" ");
                    else out.print(ne[n1++]+" ");
                }
                else if(s[i].charAt(0)=='-')
                {
                    neg=true;
                    pos=false;
                    out.print(s[i]+" ");
                }
                else if(s[i].charAt(0)=='+')
                {
                    pos=true;
                    neg=false;
                    out.print(s[i]+" ");
                }
                else if(s[i].charAt(0)=='=')
                {
                    out.print(s[i]+" ");
                    i++;
                    out.print(s[i]);
                }
            }
        }
        
        //////////////////////////////////////////////////////////////////////////////////////
        out.flush();
	out.close();
    }
    
    
    
    
    ///////////////////////////////////////////////////////////////////////////////
    
    private static long gcd(long a,long b)
    {
        if(b==0)
            return a;
        return gcd(b,a%b);
    }
    private static class pair implements Comparable<pair>
    {
        int first;
        int second;
        pair()
        {
            first=0;
            second=0;
        }
        pair(int f,int s)
        {
            first=f;
            second=s;
        }
 
        public int compareTo(pair o)
        {
            if(second>  o.second)
                return 1;
            else if(second < o.second)
                return -1;
            else
                return 0;
        }
    }
    
    public static Integer ni() throws Exception
    {
        if(!st.hasMoreTokens())
            st=new StringTokenizer(br.readLine());
        return Integer.parseInt(st.nextToken());
    }
    public static BigInteger nb()throws Exception
    {
        if(!st.hasMoreElements())
            st=new StringTokenizer(br.readLine());
        return BigInteger.valueOf(Long.parseLong(st.nextToken()));
    }
    public static Long nl() throws Exception
    {
        if(!st.hasMoreTokens())
            st=new StringTokenizer(br.readLine());
        return Long.parseLong(st.nextToken());
    }
    public static Double nd()throws Exception
    {
        if(!st.hasMoreElements())
            st=new StringTokenizer(br.readLine());
        return Double.parseDouble(st.nextToken());
    }
    public static String ns()throws Exception
    {
        if(!st.hasMoreElements())
            st=new StringTokenizer(br.readLine());
        return st.nextToken();
    }
}