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.BufferedWriter;
import java.io.FileInputStream;
import java.io.FileWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.HashMap;
import java.util.List;
import java.util.PriorityQueue;
import java.util.Queue;

public class Main {
	public static void main(String[] args) throws NumberFormatException,
	IOException {Main solve = new Main();solve.solve();}
	void dump(int[]a){for(int i=0;i<a.length;i++)System.out.print(a[i]+" ");System.out.println();}
	void dump(int[]a,int n){for(int i=0;i<a.length;i++)System.out.printf("%"+n+"d",a[i]);System.out.println();}
	void dump(long[]a){for(int i=0;i<a.length;i++)System.out.print(a[i]+" ");System.out.println();}
	void dump(char[]a){for(int i=0;i<a.length;i++)System.out.print(a[i]);System.out.println();}
	long pow(long a,int n){long r=1;while(n>0){if((n&1)==1)r*=a;a*=a;n>>=1;}return r;}
	String itob(int a,int l){return String.format("%"+l+"s",Integer.toBinaryString(a)).replace(' ','0');}
	int binarySearchSmallerMax(int[]a,int v) // get maximum index which a[idx]<=v
	{int l=0,r=a.length-1,s=0;while(l<=r){int m=(l+r)/2;if(a[m]>v)r=m-1;else{l=m+1;s=m;}}return a[s]>v?-1:s;}
	void solve() throws NumberFormatException, IOException{
		final ContestScanner in = new ContestScanner();
		Writer out = new Writer();
		List<String> str = new ArrayList<>();
		String token;
		int plus = 0;
		int minus = 0;
		while(!(token = in.nextToken()).matches("\\d+")){
			if(token.equals("-")) minus++;
			else if(token.equals("+")) plus++;
			str.add(token);
		}
		int n = Integer.parseInt(token);
//		if(minus>plus*n || (plus+1)>minus*n+n){
//			System.out.println("Impossible");
//			return;
//		}
		plus++;
		int[] resPlus = new int[plus];
		int[] resMinus = new int[minus];
		for(int i=0; i<plus; i++) resPlus[i] = n;
		for(int i=0; i<minus; i++) resMinus[i] = n;
		if(plus>minus){
			int dist = (plus - minus)*n-n;
			for(int i=0; i<plus && dist>0; i++){
				int sub = Math.min(n-1, dist);
				dist -= sub;
				resPlus[i] -= sub;
			}
			if(dist>0){
				System.out.println("Impossible");
				return;
			}
		}else if(plus<=minus){
			int dist = (minus - plus)*n+n;
			for(int i=0; i<minus && dist>0; i++){
				int sub = Math.min(n-1, dist);
				dist -= sub;
				resMinus[i] -= sub;
			}
			if(dist>0){
				System.out.println("Impossible");
				return;
			}
		}
		String bf = "+";
		int size = str.size();
		for(int i=0; i<size-1; i++){
			if(i%2==1){
				bf = str.get(i);
				continue;
			}
			if(bf.equals("+")){
				str.set(i, String.valueOf(resPlus[--plus]));
			}else{
				str.set(i, String.valueOf(resMinus[--minus]));
			}
		}
		String res = "";
		for(int i=0; i<size; i++){
			res += str.get(i)+" ";
		}
		System.out.println("Possible");
		System.out.println(res+n);
	}
}

class MultiSet<T> extends HashMap<T, Integer>{
	@Override
	public Integer get(Object key){return containsKey(key)?super.get(key):0;}
	public void add(T key,int v){put(key,get(key)+v);}
	public void add(T key){put(key,get(key)+1);}
	public void sub(T key)
	{final int v=get(key);if(v==1)remove(key);else put(key,v-1);}
}
class Timer{
	long time;
	public void set(){time=System.currentTimeMillis();}
	public long stop(){return time=System.currentTimeMillis()-time;}
	public void print()
	{System.out.println("Time: "+(System.currentTimeMillis()-time)+"ms");}
	@Override public String toString(){return"Time: "+time+"ms";}
}
class Writer extends PrintWriter{
	public Writer(String filename)throws IOException
	{super(new BufferedWriter(new FileWriter(filename)));}
	public Writer()throws IOException{super(System.out);}
}
class ContestScanner {
	private InputStreamReader in;private int c=-2;
	public ContestScanner()throws IOException 
	{in=new InputStreamReader(System.in);}
	public ContestScanner(String filename)throws IOException
	{in=new InputStreamReader(new FileInputStream(filename));}
	public String nextToken()throws IOException {
		StringBuilder sb=new StringBuilder();
		while((c=in.read())!=-1&&Character.isWhitespace(c));
		while(c!=-1&&!Character.isWhitespace(c)){sb.append((char)c);c=in.read();}
		return sb.toString();
	}
	public String readLine()throws IOException{
		StringBuilder sb=new StringBuilder();if(c==-2)c=in.read();
		while(c!=-1&&c!='\n'&&c!='\r'){sb.append((char)c);c=in.read();}
		return sb.toString();
	}
	public long nextLong()throws IOException,NumberFormatException
	{return Long.parseLong(nextToken());}
	public int nextInt()throws NumberFormatException,IOException
	{return(int)nextLong();}
	public double nextDouble()throws NumberFormatException,IOException 
	{return Double.parseDouble(nextToken());}
}