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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Washoum
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        inputClass in = new inputClass(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        BRebus solver = new BRebus();
        solver.solve(1, in, out);
        out.close();
    }

    static class BRebus {
        public void solve(int testNumber, inputClass sc, PrintWriter out) {
            String[] s = sc.nextLine().split(" ");
            int size = s.length;
            int n = Integer.parseInt(s[size - 1]);
            int nbplus = 1;
            int nbmoin = 0;
            for (int i = 1; i < size; i++) {
                if (s[i].equals("+")) {
                    nbplus++;
                } else if (s[i].equals("-")) {
                    nbmoin++;
                }
            }
            int max = nbplus * n - nbmoin;
            int min = (nbmoin * n * -1) + nbplus;
            if (n > max || n < min) {
                out.println("Impossible");
                return;
            }

            out.println("Possible");
            int sum = 0;
            int p;
            for (int i = 0; i < size - 2; i += 2) {
                p = 1;
                if (i > 0 && s[i - 1].equals("-"))
                    p = -1;
                if (p == 1) nbplus--;
                else nbmoin--;

                for (int j = 1; j <= n; j++) {
                    max = sum + p * j + nbplus * n - nbmoin;
                    min = sum + p * j + (nbmoin * n * -1) + nbplus;
                    if (n > max || n < min) {
                        continue;
                    } else {
                        out.print(j + " " + s[i + 1] + " ");
                        sum += j * p;
                        break;
                    }
                }
            }
            out.println(" " + n);

        }

    }

    static class inputClass {
        BufferedReader br;

        public inputClass(InputStream in) {

            br = new BufferedReader(new InputStreamReader(in));
        }

        public String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }

    }
}

