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.ArrayList;
import java.util.StringTokenizer;

public class Main {
    private NotMyScanner in;
    private PrintWriter out;
//    private Timer timer = new Timer();

    public static void main(String[] args) throws IOException {
        new Main().run();
    }

    int lmin, lmax, rmin, rmax;

    boolean check(int x) {
        return lmin <= x && x <= lmax && rmin <= x && x <= rmax;
    }

    private void solve() throws IOException {
        String l = in.nextLine();
        String[] a = l.split(" ");
        int n = Integer.valueOf(a[a.length - 1]);
        ArrayList<Integer> pos = new ArrayList<>(), neg = new ArrayList<>();
        pos.add(0);
        for (int i = 1; i < a.length - 1; i++) {
            if (a[i].equals("+")) {
                if (a[i + 1].equals("?")) {
                    pos.add(i + 1);
                }
            } else if (a[i].equals("-")) {
                if (a[i + 1].equals("?")) {
                    neg.add(i + 1);
                }
            }
        }
        lmin = pos.size();
        lmax = pos.size() * n;

        rmin = n + neg.size();
        rmax = n + n * neg.size();

        System.err.println(lmin + " " + lmax);
        System.err.println(rmin + " " + rmax);

        int res = -1;
        if (check(lmin)) {
            res = lmin;
        }
        if (check(lmax)) {
            res = lmax;
        }
        if (check(rmin)) {
            res = rmin;
        }
        if (check(rmax)) {
            res = rmax;
        }
        if (res == -1) {
            out.println("Impossible");
        } else {
            out.println("Possible");
            System.err.println(res);
            int need = res;
            for (int i = 0; i < pos.size(); i++) {
                int cur = Math.min(need - (pos.size() - 1 - i), n);
                a[pos.get(i)] = "" + cur;
                need -= cur;
            }
            need = res - n;
            for (int i = 0; i < neg.size(); i++) {
                int cur = Math.min(need - (neg.size() - 1 - i), n);
                a[neg.get(i)] = "" + cur;
                need -= cur;
            }
            for (String s : a) {
                out.print(s + " ");
            }
            out.println();
        }
    }

/*
    int ds = 12 * 31 * 24 * 60;
    int[] tree = new int[2 * ds];

    int getSum() {
        return tree[1];
    }

    void inc(int pos, int v) {
        pos += ds;
        while (pos > 0) {
            tree[pos] += v;
            pos /= 2;
        }
    }

    private void solve() throws IOException {
        int n = in.nextInt();
        while (n-- > 0) {
            String[] d = in.nextLine().split(" |\\.|:");
            int day = (Integer.valueOf(d[2]) - 1) * 31 + Integer.valueOf(d[1]) - 1;
            int hour = day * 24 + Integer.valueOf(d[3]);
            int min = hour * 60 + Integer.valueOf(d[4]);
            out.println(min);
            inc(min, Integer.valueOf(d[0]));
            out.println(Math.min(0, getSum()));
        }
    }*/

    private void run() throws IOException {
//        in = new NotMyScanner("B-small-attempt0.in");
        in = new NotMyScanner();
//        out = new PrintWriter(new FileOutputStream("res"), false);
        out = new PrintWriter(System.out, false);
        solve();
        out.close();
    }
}

class NotMyScanner {
    private final BufferedReader br;
    private StringTokenizer st;
    private String last;

    public NotMyScanner() {
        br = new BufferedReader(new InputStreamReader(System.in));
    }

    public NotMyScanner(String path) throws IOException {
        br = new BufferedReader(new FileReader(path));
    }

    public NotMyScanner(String path, String decoder) throws IOException {
        br = new BufferedReader(new InputStreamReader(new FileInputStream(path), decoder));
    }

    String next() throws IOException {
        while (st == null || !st.hasMoreElements())
            st = new StringTokenizer(br.readLine());
        last = null;
        return st.nextToken();
    }

    String nextLine() throws IOException {
        st = null;
        return (last == null) ? br.readLine() : last;
    }

    boolean hasNext() {
        if (st != null && st.hasMoreElements())
            return true;

        try {
            while (st == null || !st.hasMoreElements()) {
                last = br.readLine();
                st = new StringTokenizer(last);
            }
        } catch (Exception e) {
            return false;
        }

        return true;
    }

    String[] nextStrings(int n) throws IOException {
        String[] arr = new String[n];
        for (int i = 0; i < n; i++)
            arr[i] = next();
        return arr;
    }

    String[] nextLines(int n) throws IOException {
        String[] arr = new String[n];
        for (int i = 0; i < n; i++)
            arr[i] = nextLine();
        return arr;
    }

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

    int[] nextInts(int n) throws IOException {
        int[] arr = new int[n];
        for (int i = 0; i < n; i++)
            arr[i] = nextInt();
        return arr;
    }

    Integer[] nextIntegers(int n) throws IOException {
        Integer[] arr = new Integer[n];
        for (int i = 0; i < n; i++)
            arr[i] = nextInt();
        return arr;
    }

    int[][] next2Ints(int n, int m) throws IOException {
        int[][] arr = new int[n][m];
        for (int i = 0; i < n; i++)
            for (int j = 0; j < m; j++)
                arr[i][j] = nextInt();
        return arr;
    }

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

    long[] nextLongs(int n) throws IOException {
        long[] arr = new long[n];
        for (int i = 0; i < n; i++)
            arr[i] = nextLong();
        return arr;
    }

    long[][] next2Longs(int n, int m) throws IOException {
        long[][] arr = new long[n][m];
        for (int i = 0; i < n; i++)
            for (int j = 0; j < m; j++)
                arr[i][j] = nextLong();
        return arr;
    }

    double nextDouble() throws IOException {
        return Double.parseDouble(next().replace(',', '.'));
    }

    double[] nextDoubles(int size) throws IOException {
        double[] arr = new double[size];
        for (int i = 0; i < size; i++)
            arr[i] = nextDouble();
        return arr;
    }

    boolean nextBool() throws IOException {
        String s = next();
        if (s.equalsIgnoreCase("true") || s.equals("1"))
            return true;

        if (s.equalsIgnoreCase("false") || s.equals("0"))
            return false;

        throw new IOException("Boolean expected, String found!");
    }
}