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.util.*;
import java.io.*;
import java.math.BigInteger;

public class CodeForces {

    private static int count = 1;
    private static int count2;

    public static void main(String args[]) throws IOException {
        Reader.init(System.in);
        PrintWriter write = new PrintWriter(System.out);
        String line = Reader.reader.readLine();

        for (int i = 0; i < line.length(); i++) {
            if (line.charAt(i) == '+') {
                count++;
            } else if (line.charAt(i) == '-') {
                count2++;
            }
        }

        int n = Integer.parseInt(line.substring(line.indexOf("=") + 2));
        int num = (count2 + n) / count;
        int rem = (count2 + n) % count;

        if(num > n || (num + 1 > n && rem != 0))
            write.print("Impossible");
        
        else {
            
            int zero = 0, xRem = 0, x = 1;
            
            
        if(num == 0){
            zero = count - rem;
            if(count2 != 0){
                x = zero / count2 + 1;
                 xRem = zero % count2;
            }
            
            if(x > n || (x + 1 > n && xRem!=0) || count2 == 0){
                write.print("Impossible");
                write.close();
                return;
            }
        
        }
            write.print("Possible\n");
            
            write.print(num + (rem > 0 ? 1 : 0));
            for (int i = 1; i < line.length(); i++) {
                if(line.charAt(i) == '?'){
                    if(line.charAt(i-2) == '-')
                        write.print(x + (xRem-- > 0 ? 1 : 0));
                    else{
                        int h = num;
                        rem--;
                        if(rem > 0)
                            h++;
                        else if(zero > 0){
                            h++;
                            zero--;
                        }
                        
                        write.print(h);
                    }
                }
                else
                    write.print(line.charAt(i));
            }
        }
        
        write.close();
    }
}

class Pair {

    int x, y;

    public Pair(int x, int y) {
        this.x = x;
        this.y = y;
    }

    @Override
    public boolean equals(Object o) {
        Pair p = (Pair) o;
        return (p.x == x && p.y == y) || (p.x == y || p.y == x);
    }

    @Override
    public int hashCode() {

        return ((x + 1) * (y + 1)) % ((int) 1e7 + 7);
    }

}

class Reader {

    static BufferedReader reader;
    static StringTokenizer tokenizer;

    public static int pars(String x) {
        int num = 0;
        int i = 0;
        if (x.charAt(0) == '-') {
            i = 1;
        }
        for (; i < x.length(); i++) {
            num = num * 10 + (x.charAt(i) - '0');
        }

        if (x.charAt(0) == '-') {
            return -num;
        }

        return num;
    }

    static void init(InputStream input) {
        reader = new BufferedReader(
                new InputStreamReader(input));
        tokenizer = new StringTokenizer("");
    }

    static void init(FileReader input) {
        reader = new BufferedReader(input);
        tokenizer = new StringTokenizer("");
    }

    static String next() throws IOException {
        while (!tokenizer.hasMoreTokens()) {
            tokenizer = new StringTokenizer(
                    reader.readLine());
        }
        return tokenizer.nextToken();
    }

    static int nextInt() throws IOException {
        return pars(next());
    }

    static long nextLong() throws IOException {
        return Long.parseLong(next());
    }

    static double nextDouble() throws IOException {
        return Double.parseDouble(next());
    }
}
