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.*;



public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        Task solver = new Task();
        solver.solve(in, out);
        out.close();
    }
}



class Task {

    List<Boolean> order = new ArrayList<>();

    public void solve(InputReader in, OutputWriter out) {
        Scanner scanner  = new Scanner(System.in);
        String line = scanner.nextLine();
        int questions = 0;
        int i = 0;
        order.add(true);
        while(true) {
            if(line.charAt(i) == '-') {
                order.add(false);
            } else if(line.charAt(i) == '+') {
                order.add(true);
            }
            else if(line.charAt(i) == '?') questions++;
            else if(line.charAt(i) == '=') break;
            i++;
        }

        Map<Integer, String> map = new HashMap<>();


        for (Map.Entry<Integer, String> entry : map.entrySet()) {
            
        }
        
        i+=2;
        int number = Integer.parseInt(line.substring(i));
        int numbers[] = new int[questions];
        int m = 0;
        for(int j=0;j<numbers.length;j++) {
            if(order.get(j)) {
                numbers[j] = 1;
                m++;
            } else {
                numbers[j] = -1;
                m--;
            }
        }
        if(m >= number) {
            for(int j=0;j<numbers.length;j++) {
                if(!order.get(j)) {
                    int p = Math.min(m - number, number - 1);
                    numbers[j] -= p;
                    m -= p;
                }
            }
        } else {
            for(int j=0;j<numbers.length;j++) {
                if(order.get(j)) {
                    int p = Math.min(number - m, number - 1);
                    numbers[j] += p;
                    m += p;
                }
            }
        }

        if(m != number) {
            out.printLine("Impossible");
        } else {
            out.printLine("Possible");
            out.print(numbers[0]);
            for(int j=1;j<numbers.length;j++) {
                if(order.get(j)) {
                    out.print(" + " + numbers[j]);
                } else {
                    out.print(" - " + Math.abs(numbers[j]));
                }
            }
            out.print(" = " + number);
        }

    }



}

class InputReader {
    public BufferedReader reader;
    public StringTokenizer tokenizer;
    public InputReader(InputStream stream) {
        reader = new BufferedReader(new InputStreamReader(stream), 32768);
        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 boolean hasNext() {
        while (tokenizer == null || !tokenizer.hasMoreTokens()) {
            try {
                String line = reader.readLine();
                if ( line == null ) {
                    return false;
                }
                tokenizer = new StringTokenizer(line);
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
        return true;
    }
    public int nextInt() {
        return Integer.parseInt(next());
    }

    public long nextLong() {
        return Long.parseLong(next());
    }

    public double nextDouble() { return Double.parseDouble(next());}
}
class OutputWriter {
    private final PrintWriter writer;
    public OutputWriter(OutputStream outputStream) {
        writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
    }
    public OutputWriter(Writer writer) {
        this.writer = new PrintWriter(writer);
    }
    public void print(Object... objects) {
        for (int i = 0; i < objects.length; i++) {
            if ( i != 0 ) {
                writer.print(' ');
            }
            writer.print(objects[i]);
        }
    }
    public void printLine(Object... objects) {
        print(objects);
        writer.println();
    }
    public void close() {
        writer.close();
    }
}