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.math.BigDecimal;
import java.math.BigInteger;
import java.util.*;

public class Template implements Runnable {

    BufferedReader in;
    PrintWriter out;
    StringTokenizer tok = new StringTokenizer("");

    void init() throws FileNotFoundException {
        try {
            in = new BufferedReader(new FileReader("input.txt"));
            out = new PrintWriter("output.txt");
        } catch (Exception e) {
            in = new BufferedReader(new InputStreamReader(System.in));
            out = new PrintWriter(System.out);
        }
    }

    String readString() throws IOException {
        while (!tok.hasMoreTokens()) {
            try {
                tok = new StringTokenizer(in.readLine(), " :");
            } catch (Exception e) {
                return null;
            }
        }
        return tok.nextToken();
    }

    int readInt() throws IOException {
        return Integer.parseInt(readString());
    }

    int[] readIntArray(int size) throws IOException {
        int[] res = new int[size];
        for (int i = 0; i < size; i++) {
            res[i] = readInt();
        }
        return res;
    }

    long readLong() throws IOException {
        return Long.parseLong(readString());
    }

    double readDouble() throws IOException {
        return Double.parseDouble(readString());
    }

    <T> List<T>[] createGraphList(int size) {
        List<T>[] list = new List[size];
        for (int i = 0; i < size; i++) {
            list[i] = new ArrayList<>();
        }
        return list;
    }

    public static void main(String[] args) {
        new Thread(null, new Template(), "", 1l * 200 * 1024 * 1024).start();
    }

    long timeBegin, timeEnd;

    void time() {
        timeEnd = System.currentTimeMillis();
        System.err.println("Time = " + (timeEnd - timeBegin));
    }

    long memoryTotal, memoryFree;

    void memory() {
        memoryFree = Runtime.getRuntime().freeMemory();
        System.err.println("Memory = " + ((memoryTotal - memoryFree) >> 10)
                + " KB");
    }

    public void run() {
        try {
            timeBegin = System.currentTimeMillis();
            memoryTotal = Runtime.getRuntime().freeMemory();
            init();
            solve();
            out.close();
            if (System.getProperty("ONLINE_JUDGE") == null) {
                time();
                memory();
            }
        } catch (Exception e) {
            e.printStackTrace();
            System.exit(-1);
        }
    }

    int[] p;

    int find(int x) {
        if (x == p[x]) return x;
        return p[x] = find(p[x]);
    }

    void merge(int x, int y) {
        x = find(x);
        y = find(y);
        if (new Random().nextBoolean()) {
            p[x] = y;
        } else {
            p[y] = x;
        }
    }


    void solve() throws IOException {
        String s = in.readLine();
        StringTokenizer tok = new StringTokenizer(s);
        List<Boolean> signs = new ArrayList<>();
        signs.add(true);
        int n;
        while (true) {
            String token = tok.nextToken();
            if (token.equals("?")) continue;
            if (token.equals("+")) {
                signs.add(true);
            } else if (token.equals("-")) {
                signs.add(false);
            } else {
                n = Integer.parseInt(tok.nextToken());
                break;
            }
        }
        int size = signs.size();
        int[] values = new int[size];
        boolean[] mult = new boolean[size];
        for (int i = 0; i < size; i++) {
            mult[i] = signs.get(i);
        }
        Arrays.fill(values, n);
        int current = 0;
        for (int i = 0; i < size; i++) {
            if (mult[i]) current += n;
            else current -= n;
        }

        for (int i = 0; i < size; i++) {
            if (mult[i]) {
                if (current > n) {
                    int dec = Math.min(n - 1, current - n);
                    values[i] -= dec;
                    current -= dec;
                }
            } else {
                if (current < n) {
                    int inc = Math.min(n - 1, n - current);
                    values[i] -= inc;
                    current += inc;
                }
            }
        }
        if (current == n) {
            out.println("Possible");
            for (int i = 0; i < size; i++) {
                if (i != 0) out.print(mult[i] ? "+ " : "- ");
                out.print(values[i] + " ");
            }
            out.println("= " + n);
        } else {
            out.println("Impossible");
        }

    }


}