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.BufferedReader;
import java.io.File;
import java.io.FileNotFoundException;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.List;
import java.util.StringTokenizer;
import java.util.function.Supplier;

import static java.lang.String.valueOf;
import static java.util.Arrays.asList;
import static java.util.Collections.nCopies;

public class B {
    public String solve(String s) {
        List<String> tokens = asList(s.split(" "));
        int last = Integer.valueOf(tokens.get(tokens.size() - 1));
        long pluses = tokens.stream().filter(string -> string.equals("+")).count();
        long minuses = tokens.stream().filter(string -> string.equals("-")).count();
        long max = (pluses + 1) * last - minuses;
        long min = minuses * (-last) + (pluses + 1);

        if (min <= last && last <= max) {
            List<Long> positive = new ArrayList<>(nCopies((int)pluses + 1, 1L));
            List<Long> negative = new ArrayList<>(nCopies((int)minuses, 1L));
            int curp = 0;
            int curn = 0;
            long sum = positive.stream().reduce(0L, Long::sum) - negative.stream().reduce(0L, Long::sum);
            while (sum != last) {
                if (sum < last) {
                    long incr = Math.min(last - sum, last - positive.get(curp));
                    positive.set(curp, positive.get(curp) + incr);
                    curp++;
                } else {
                    long decr = Math.min(sum - last, last - negative.get(curn));
                    negative.set(curn, positive.get(curn) + decr);
                    curn++;
                }
                sum = positive.stream().reduce(0L, Long::sum) - negative.stream().reduce(0L, Long::sum);
            }
            s = s.replaceFirst("\\?", valueOf(positive.get(0)));
            for (int i = 0; i < pluses; i++) {
                s = s.replaceFirst("\\+ \\?", "+ " + valueOf(positive.get(i + 1)));
            }
            for (int i = 0; i < minuses; i++) {
                s = s.replaceFirst("\\- \\?", "- " + valueOf(negative.get(i)));
            }
            return s;
        } else {
            return null;
        }
    }

    public static void main(String[] args) throws IOException {
        FastScanner sc = new FastScanner(System.in);
        PrintWriter pw = new PrintWriter(System.out);

        // read data
        String res = new B().solve(sc.nextLine());

        if (res == null) {
            pw.println("Impossible");
        } else {
            pw.println("Possible");
            pw.println(res);
        }

        pw.flush();
    }

    static class FastScanner {
        private BufferedReader br;
        private StringTokenizer st;

        FastScanner(File f) throws FileNotFoundException {
            br = new BufferedReader(new FileReader(f));
        }

        FastScanner(InputStream stream) {
            br = new BufferedReader(new InputStreamReader(stream));
        }

        public String next() {
            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public long nextLong() {
            return Long.parseLong(next());
        }

        public String nextLine() throws IOException {
            st = null; // meh
            return br.readLine();
        }
    }
}
