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.BufferedWriter;
import java.util.InputMismatchException;
import java.util.ArrayList;
import java.io.InputStream;
import java.io.OutputStreamWriter;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.Writer;
import java.io.IOException;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 * @author ilyakor
 */
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);
		TaskA solver = new TaskA();
		solver.solve(1, in, out);
		out.close();
	}
}

class TaskA {
    public void solve(int testNumber, InputReader in, OutputWriter out) {
        String s = in.nextLine();
        String[] parts = s.split("\\s+");
        int n = Integer.parseInt(parts[parts.length - 1]);
        int cnt = (parts.length - 1) / 2;
        ArrayList<Integer> plusPos = new ArrayList<>();
        ArrayList<Integer> minusPos = new ArrayList<>();
        plusPos.add(-1);
        for (int i = 0; i < cnt - 1; ++i) {
            if (parts[i * 2 + 1].equals("+"))
                plusPos.add(i);
            else
                minusPos.add(i);
        }
        int lP = plusPos.size(), rP = plusPos.size() * n;
        int lM = minusPos.size(), rM = minusPos.size() * n;
        if (n < lP - rM || n > rP - lM) {
            out.printLine("Impossible");
            return;
        }
        out.printLine("Possible");
        int px = lP, py;
        while (true) {
            py = px - n;
            if (py >= lM && py <= rM)
                break;
            ++px;
        }
        for (int i = 0; i < plusPos.size(); ++i) {
            int val = Math.max(1, px - n * (plusPos.size() - i - 1));
            parts[plusPos.get(i) * 2 + 2] = "" + val;
            px -= val;
        }
        for (int i = 0; i < minusPos.size(); ++i) {
            int val = Math.max(1, py - n * (minusPos.size() - i - 1));
            parts[minusPos.get(i) * 2 + 2] = "" + val;
            py -= val;
        }
        for (String part : parts)
            out.print(part + " ");
        out.printLine();
    }
}

class InputReader {
    private InputStream stream;
    private byte[] buffer = new byte[10000];
    private int cur;
    private int count;

    public InputReader(InputStream stream) {
        this.stream = stream;
    }

    public static boolean isSpace(int c) {
        return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
    }

    public int read() {
        if (count == -1) {
            throw new InputMismatchException();
        }
        try {
            if (cur >= count) {
                cur = 0;
                count = stream.read(buffer);
                if (count <= 0)
                    return -1;
            }
        } catch (IOException e) {
            throw new InputMismatchException();
        }
        return buffer[cur++];
    }

    public int readSkipSpace() {
        int c;
        do {
            c = read();
        } while (isSpace(c));
        return c;
    }

    public String nextLine() {
        int c = readSkipSpace();
        StringBuilder sb = new StringBuilder();
        while (c != '\n' && c != -1) {
            sb.append((char)c);
            c = read();
        }
        return sb.toString();
    }

}

class OutputWriter {
    private final PrintWriter writer;

    public OutputWriter(OutputStream outputStream) {
        writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
    }

    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();
    }

}

