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.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Random;
import java.util.StringTokenizer;

public class Solution{
	
	
    public static void main(String[] args) throws IOException {
     
    	FastScanner fs = new FastScanner();
    	PrintWriter out = new PrintWriter(System.out);
    	
    		
    		
    	int tt = 1;
    	while(tt-->0) {
    	
    		ArrayList<Integer> list = new ArrayList<Integer>();
    		String str = fs.nextLine();
    		int n = 0;
    		
    		list.add(0);
    		for(int i=0;i<str.length();i++) {
    			if(str.charAt(i)=='+') list.add(0);
    			else if(str.charAt(i)=='-') list.add(1);
    			else if(str.charAt(i)=='=') {
    				String s = "";
    				for(int j=i+2;j<str.length();j++) s+= str.charAt(j);
    				n = Integer.parseInt(s);
    			}
    		}
    		
    		
    		int cnt1 = 0;  //number of positives
    		int cnt2 = 0;  //number of negatives
    		
    		for(int i=0;i<list.size();i++) {
    			if(list.get(i)==0) cnt1++;
    			else cnt2++;
    		}
    		
    		if(n+cnt2>n*cnt1) {
    			out.println("Impossible");
    			out.flush();
    			return;
    		}
    		if(n+n*cnt2<cnt1) {
    			out.println("Impossible");
    			out.flush();
    			return;
    		}
    		
    		int d = -1;
    		int s = -1;
    		
    		if(contains(n+cnt2, cnt1, n*cnt1))  d = cnt2; 
    		else if(contains(n+n*cnt2, cnt1, n*cnt1)) d = n*cnt2;
    		else if(contains(cnt1, n+cnt2, n+n*cnt2)) d = cnt1-n; 
    		else if(contains(n*cnt1, n+cnt2, n+n*cnt2)) d = n*cnt1 - n; 
    			
    		
    		s = n + d;
    		
    		ArrayList<Integer> pos = new ArrayList<Integer>();
    		ArrayList<Integer> neg = new ArrayList<Integer>();
    		
    		
    		for(int i=0;i<s%cnt1;i++) pos.add(s/cnt1+1);
    		for(int i=s%cnt1;i<cnt1;i++) pos.add(s/cnt1);
    		
    		if(cnt2!=0) for(int i=0;i<d%cnt2;i++) neg.add(d/cnt2+1);
    		if(cnt2!=0) for(int i=d%cnt2;i<cnt2;i++) neg.add(d/cnt2);
    		
    		out.println("Possible");
    		
    		int cur1 = 0, cur2 = 0;
    		out.print(pos.get(cur1++)+" ");
    		
    		for(int i=1;i<list.size();i++) {
    			out.print((list.get(i)==0?'+':'-')+" ");
    			out.print(((list.get(i)==0)?pos.get(cur1++):neg.get(cur2++))+" ");
    		}
    		
    		out.println("= "+n);
    		
    		
    		
    		
    	}
    	
    		
    		
    		
    	out.close();
    		
    }
    
    
	
    static boolean contains(int a, int b, int c) {
    	if(a>=b && a<=c) return true;
    	return false;
    }
    
    
    
    
    static final Random random=new Random();
    	
    static void ruffleSort(int[] a) {
    	int n=a.length;//shuffle, then sort 
    	for (int i=0; i<n; i++) {
    		int oi=random.nextInt(n); int temp=a[oi];
    		a[oi]=a[i]; a[i]=temp;
    	}
    	Arrays.sort(a);
    }
   
  
    
    	
    	
    static class FastScanner{
    	BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    	StringTokenizer st = new StringTokenizer("");
     
    	public String next(){
    		while(!st.hasMoreElements()){
    			try{
    				st = new StringTokenizer(br.readLine());
    			} catch(IOException e){
    				e.printStackTrace();
    			}
    		}
    		return st.nextToken();
    	}
    		
    	public String nextLine() throws IOException {
    		return br.readLine();
    	}
    		
    	public int nextInt(){
    		return Integer.parseInt(next());
    	}
     
    	public int[] readArray(int n){
    		int[] a = new int[n];
    		for(int i=0;i<n;i++)
    			a[i] = nextInt();
    		return a;
    	}
    		
    	public long nextLong() {
    		return Long.parseLong(next());
    	}
    		
    	public char nextChar() {
    		return next().toCharArray()[0];
    	}
    }
   	
}