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

/**
 * @author kunal05
 */

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.StringTokenizer;

public class B {
	public static void main(String[] args) {
		InputReader in = new InputReader();
		PrintWriter out = new PrintWriter(System.out);
		final long start = System.currentTimeMillis();		
		new Task1().solve(in, out);
		@SuppressWarnings("unused")
		final long duration = System.currentTimeMillis()-start;
		out.close();
	}

	static class Task1{
		static final int PLUS	= -1000001;
		static final int MINUS	= -1000002;
		static final int SPACE	= -1000003;
		boolean positive;
		public void solve(InputReader in, PrintWriter out){
			String s = in.nextLine();
			positive = true;
			ArrayList<Integer> answer = new ArrayList<Integer>();

			int pos=0, neg=0, ii=0, last_pos_pve =0, last_pos_nve = -1;

			while(s.charAt(ii) != '='){
				if(s.charAt(ii) == '?'){
					answer.add(1);
					if(positive){
						pos++;
						last_pos_pve = ii;
					} else {
						neg++;
						last_pos_nve = ii;
					}
				} else if (s.charAt(ii) == '+') {
					positive = true;
					answer.add(PLUS);
				} else if (s.charAt(ii) == '-') {
					positive = false;
					answer.add(MINUS);
				} else {
					answer.add(SPACE);
				}
				ii++;
			}
			Integer n = Integer.parseInt(s.substring(ii+2));
			
			if(!check(pos, neg, n)){
				out.println("Impossible");
				return;
			}

			int balance=0, quo=0, rem=0, it, offset = 0;
			

			// cases possible
			/**
			 * Important point : Should not print zero.. so if balance == 0.. must be set to something
			 * Use offset
			*/
			if (pos <= n || (neg > (pos-n))) {
				/*	- Then we need to balance positives.
					- i.e., set all neg to 1 (effectively -1) and sum of negatives will be neg
						quo = (neg + n)/pos;
						remaining balance = (neg + n)%pos;
					- Set all pos to quo
					- Traverse for all positive numbers and increment each by 1 till balance != 0
				*/
				balance = n+neg;
				quo = balance/pos;
				balance = balance%pos;
				
				positive = true;
				for (int i=0; i<answer.size(); i++) {
					it = answer.get(i);
					if (it == SPACE) {
						continue;
					} else if (it == MINUS) {
						positive = false;
						continue;
					} else if (it == PLUS) {
						positive = true;
						continue;
					} else {
						if (positive) {
							answer.set(i, quo);
						} else {
							answer.set(i, 1);
						}
					}
				}

				positive = true;
				for(int i=0; i<answer.size(); i++){
					if(balance == 0){
						break;
					}
					it = answer.get(i);
					if (it == PLUS) {
						positive = true;
					} else if (it == MINUS) {
						positive = false;
					} else if (it == SPACE) {
						//
					} else{
						if(positive){
							answer.set(i, quo+1);
							balance--; 
						}
					}
				}
			} else if (pos>n) {
				//System.out.println(" I am here");
				/*	- Then we need to balance negatives but all negative should be atleast 1
					- i.e., set all pos to 1 (effectively +1) and sum of positives will be pos
						quo = (pos + n)/neg;
						rem = (pos + n)%neg;
					- Set all neg to quo
					- Traverse for all negative numbers and increment each by 1 til balance != 0
				*/
				balance = pos-n;
				quo = balance/neg;
				balance = balance%neg;
				
				positive = true;
				for (int i=0; i<answer.size(); i++) {
					it = answer.get(i);
					if (it == SPACE) {
						continue;
					} else if (it == MINUS) {
						positive = false;
						continue;
					} else if (it == PLUS) {
						positive = true;
						continue;
					} else {
						if (positive) {
							answer.set(i, 1);
						} else {
							answer.set(i, quo);
						}
					}
				}

				positive = true;
				for(int i=0; i<answer.size(); i++){
					if(balance == 0){
						break;
					}
					it = answer.get(i);
					if (it == PLUS) {
						positive = true;
					} else if (it == MINUS) {
						positive = false;
					} else if (it == SPACE) {
						//
					} else{
						if(!positive){
							answer.set(i, quo+1);
							balance--; 
						}
					}
				}
			} 

			// printing the result
			out.println("Possible");
			for(int i=0; i<answer.size(); i++){
				it = answer.get(i);
				if (it == PLUS) {
					out.print("+");
				} else if(it == MINUS) {
					out.print("-");
				} else if(it == SPACE) {
					out.print(" ");
				} else {
					out.print(it);
				}
			}
			out.println("= "+n);

		}

		static boolean check(int positive_count, int negative_count, int n){
			int min = positive_count - negative_count*n;
			int max = positive_count*n - negative_count;
			return (n<=max) && (n>=min);
		}
	}
	
	static class InputReader {
		public BufferedReader reader;
		public StringTokenizer tokenizer;
		
		public InputReader() {
			reader = new BufferedReader(new InputStreamReader(System.in));
			tokenizer = null;
		}
		
		public String next() {
			while (tokenizer == null || !tokenizer.hasMoreTokens()) {
				try {
					tokenizer = new StringTokenizer(reader.readLine());
				} catch (IOException e) {
					throw new RuntimeException(e);
				}
			}
			return tokenizer.nextToken();
		}
		
		public int nextInt() {
			return Integer.parseInt(next());
		}
		
		public long nextLong() {
			return Long.parseLong(next());
		}
		
		public double nextDouble() {
			return Double.parseDouble(next());
		}
		
		public String nextLine() {
			String s=null;
			try{
				s = reader.readLine();
			} catch(IOException e){
				throw new RuntimeException(e);
			}
			return s;
        }
		
		public String nextParagraph() {
			String line=null;
			String ans = "";
			try{
				while ((line = reader.readLine()) != null) {
				ans += line;
				}
			} catch(IOException e){
				throw new RuntimeException(e);
			}
			return ans;
		}
		
	}
}