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.*;
import java.util.InputMismatchException;

public class Cf347B {
    private static InputReader in = new InputReader(System.in);
    private static OutputWriter out = new OutputWriter(System.out);




    private static void solve() throws Exception{
        int plus = 1;
        int minus = 0;
        StringBuilder question = new StringBuilder();

        while(true) {
            String s = in.readString();

            if (s.charAt(0) == '=') {
                break;
            }

            if(s.charAt(0)== '+'){
                plus++;
            }
            if(s.charAt(0)== '-'){
                minus++;
            }
            question.append(s.charAt(0));
        }
        String ques = question.toString();
        int n = in.readInt();
        int min = plus-minus*n;
        int max = plus*n-minus;
        if((n<min)||(n>max)){
            out.println("Impossible");
        }
        else{
            out.println("Possible");
            int difference = n - min;
            plus--;
            String result ="";
            int add = Math.min(n-1,difference);
            difference -= add;
            add++;
            result += add;

            for(int i=1; i<ques.length(); i=i+2){

                if(ques.charAt(i)=='-'){
                    result = result +" - ";
                    minus--;
                    add = Math.min(n-1,difference);
                    difference -= add;
                    add = n-add;
                    result += add;
                }
                else{
                    plus--;
                    result = result +" + ";
                    add = Math.min(n-1,difference);
                    difference -= add;
                    add++;
                    result += add;
                }

            }
            result += " = ";
            result += n;
            out.println(result);


        }


    }



    public static void main(String[] args) throws Exception {
        solve();
        out.close();
    }


    private static class InputReader {
        private InputStream stream;
        private byte[] buffer;
        private int currentIndex;
        private int bytesRead;

        public InputReader(InputStream stream) {
            this.stream = stream;
            buffer = new byte[131072];
        }


        public InputReader(InputStream stream, int bufferSize) {
            this.stream = stream;
            buffer = new byte[bufferSize];
        }


        private int read() throws IOException {
            if (currentIndex >= bytesRead) {
                currentIndex = 0;
                bytesRead = stream.read(buffer);
                if (bytesRead <= 0) {
                    return -1;
                }
            }
            return buffer[currentIndex++];
        }

        public String readString() throws IOException {
            int c = read();
            while (!isPrintable(c)) {
                c = read();
            }
            StringBuilder result = new StringBuilder();
            do {
                result.appendCodePoint(c);
                c = read();
            } while (isPrintable(c));
            return result.toString();
        }

        public int readInt() throws Exception {
            int c = read();
            int sign = 1;
            while (!isPrintable(c)) {
                c = read();
            }
            if (c == '-') {
                sign = -1;
                c = read();
            }
            int result = 0;
            do {
                if ((c < '0') || (c > '9')) {
                    throw new InputMismatchException();
                }
                result *= 10;
                result += (c - '0');
                c = read();
            } while (isPrintable(c));
            return sign * result;
        }

        public long readLong() throws Exception {
            int c = read();
            int sign = 1;
            while (!isPrintable(c)) {
                c = read();
            }
            if (c == '-') {
                sign = -1;
                c = read();
            }
            long result = 0;
            do {
                if ((c < '0') || (c > '9')) {
                    throw new InputMismatchException();
                }
                result *= 10;
                result += (c - '0');
                c = read();
            } while (isPrintable(c));
            return sign * result;
        }

        public double readDouble() throws Exception {
            int c = read();
            int sign = 1;
            while (!isPrintable(c)) {
                c = read();
            }
            if (c == '-') {
                sign = -1;
                c = read();
            }
            boolean fraction = false;
            double multiplier = 1;
            double result = 0;
            do {
                if ((c == 'e') || (c == 'E')) {
                    return sign * result * Math.pow(10, readInt());
                }
                if ((c < '0') || (c > '9')) {
                    if ((c == '.') && (!fraction)) {
                        fraction = true;
                        c = read();
                        continue;
                    }
                    throw new InputMismatchException();
                }
                if (fraction) {
                    multiplier /= 10;
                    result += (c - '0') * multiplier;
                    c = read();
                } else {
                    result *= 10;
                    result += (c - '0');
                    c = read();
                }
            } while (isPrintable(c));
            return sign * result;
        }

        private boolean isPrintable(int c) {
            return ((c > 32) && (c < 127));
        }
    }

    private static class OutputWriter {
        private PrintWriter writer;

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

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void print(Object... objects) {
            for (int i = 0; i < objects.length; i++) {
                if (i != 0) {
                    writer.print(' ');
                }
                writer.print(objects[i]);
            }
        }

        public void println(Object... objects) {
            print(objects);
            writer.println();
        }

        public void close() {
            writer.close();
        }

        public void flush() {
            writer.flush();
        }
    }
}