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.StringReader;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.Reader;
import java.io.InputStreamReader;
import java.io.InputStream;

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

    static class TaskB {
        private final FastScanner in;
        private final PrintWriter out;

        public TaskB(FastScanner in, PrintWriter out) {
            this.in = in;
            this.out = out;
        }

        public void solve(int testNumber) throws IOException {
            String eq = in.readLine();
            String[] elements = eq.split(" ");
            int n = Integer.parseInt(elements[elements.length - 1]);
            int q = (elements.length - 1) / 2;
            int[] min = new int[q];
            int[] max = new int[q];
            min[q - 1] = n;
            max[q - 1] = n;
            for (int i = q - 2; i >= 0; i--) {
                int sign = elements[2 * i + 1].equals("+") ? +1 : -1;
                if (sign > 0) {
                    min[i] = min[i + 1] - n;
                    max[i] = max[i + 1] - 1;
                } else {
                    min[i] = min[i + 1] + 1;
                    max[i] = max[i + 1] + n;
                }
            }
            if (max[0] < 1 || min[0] > n) {
                out.println("Impossible");
                return;
            }

            out.println("Possible");

            int c = Math.max(1, min[0]);
            out.print(c);
            out.print(' ');
            for (int i = 1; i < q; i++) {
                int sign = elements[2 * i - 1].equals("+") ? +1 : -1;

                int x;
                if (sign > 0) {
                    x = Math.min(n, max[i] - c);
                    c += x;
                } else {
                    x = Math.min(n, c - min[i]);
                    c -= x;
                }
                if (x < 1 || x > n) {
                    throw new AssertionError();
                }
                if (c < min[i] || c > max[i]) {
                    throw new AssertionError();
                }

                out.print(elements[2 * i - 1]);
                out.print(' ');
                out.print(x);
                out.print(' ');
            }
            out.print("= ");
            out.println(n);
        }

    }

    static class FastScanner {
        private final BufferedReader br;
        private String line;
        private int pos;

        public FastScanner(String s) throws IOException {
            this(new StringReader(s));
        }

        public FastScanner(InputStream is) throws IOException {
            this(new InputStreamReader(is, "UTF-8"));
        }

        public FastScanner(Reader reader) throws IOException {
            this(new BufferedReader(reader));
        }

        public FastScanner(BufferedReader reader) throws IOException {
            br = reader;
            line = br.readLine();
            pos = 0;
        }

        public String readLine() throws IOException {
            String prevLine = line.substring(pos);
            line = br.readLine();
            pos = 0;
            return prevLine;
        }

    }
}

