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.InputStream;
import java.io.PrintStream;
import java.util.ArrayList;
import java.util.List;
import java.util.Scanner;

public class Rebus {
    public static void main(String[] args) {
        // Instantiate & RUN!!!
        Rebus instance = new Rebus();
        instance.run(System.in, System.out);
    }

    public void run(InputStream inputStream, PrintStream printStream) {
        final Scanner scan = new Scanner(inputStream);
        final List<Boolean> isPositive = new ArrayList<>();
        StringBuilder outputFormatBuilder = new StringBuilder();
        outputFormatBuilder.append("%d");
        int n = inputParser(scan, isPositive, outputFormatBuilder);
        if(isPossibleSolution(isPositive, 1, n)) {
            printStream.println("Possible");
            final List<Integer> numbers = new ArrayList<>();
            final int diff = calcOneDiff(numbers, isPositive, n);
            adjustNumbers(numbers, isPositive, diff);
            numbers.add(n);
            printStream.println(String.format(outputFormatBuilder.toString(), numbers.toArray()));
        } else {
            printStream.println("Impossible");
        }
    }

    private void adjustNumbers(List<Integer> numbers, List<Boolean> isPositive, int diff) {
        if (diff == 0) {
            return;
        }
        int numPos = 0;
        int numNeg = 0;
        for (final boolean thisNum: isPositive) {
            if(thisNum) {
                numPos++;
            } else {
                numNeg++;
            }
        }
        final boolean isDiffPositive = (diff > 0);
        if (isDiffPositive) {
            int add = diff / numPos;
            int rem = diff % numPos;
            for (int i = 0; i < isPositive.size(); i++) {
                if (isPositive.get(i)) {
                    int n = numbers.get(i);
                    if (rem > 0) {
                        rem--;
                        n += add + 1;
                    } else {
                        n += add;
                    }
                    numbers.set(i, n);
                }
            }
        } else {
            diff = -1 * diff;
            int add = diff / numNeg;
            int rem = diff % numNeg;
            for (int i = 0; i < isPositive.size(); i++) {
                if (!isPositive.get(i)) {
                    int n = numbers.get(i);
                    if (rem > 0) {
                        rem--;
                        n += add + 1;
                    } else {
                        n += add;
                    }
                    numbers.set(i, n);
                }
            }
        }
    }

    private int calcOneDiff(List<Integer> numbers, List<Boolean> isPositive, int n) {
        int runningSum = 0;
        for(final boolean thisNum: isPositive) {
            numbers.add(1);
            if(thisNum) {
                runningSum++;
            } else {
                runningSum--;
            }
        }
        return n - runningSum;
    }

    private boolean isPossibleSolution(List<Boolean> isPositive, int start, int n) {
        int posMin = 0;
        int posMax = 0;
        for (final boolean thisNum: isPositive) {
            if(thisNum) {
                posMin += start;
                posMax += n;
            } else {
                posMin -= n;
                posMax -= start;
            }
        }
        return ((posMin <= n) && (n <= posMax));
    }

    private int inputParser(Scanner scan, List<Boolean> isPositive, StringBuilder outputFormatBuilder) {
        int returnInt = 0;
        isPositive.add(true);
        scan.next();
        while(scan.hasNext()) {
            switch (scan.next()) {
                case "+" :
                    outputFormatBuilder.append(" + %d");
                    isPositive.add(true);
                    scan.next();
                    break;
                case "-":
                    outputFormatBuilder.append(" - %d");
                    isPositive.add(false);
                    scan.next();
                    break;
                case "=":
                    returnInt = scan.nextInt();
                    outputFormatBuilder.append( " = ").append(returnInt);
                    break;
            }
        }
        return returnInt;
    }
}
