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.*;

public class Task3 {

    public static void main(String[] args) throws IOException {

        new Task3().solve();
    }

    int mod = 1000000007;

    PrintWriter out;

    int n;
    int m;

    long inf = Long.MAX_VALUE;

    //int[][] g = new int[110][110];

    int max = 0;

    long base = (1L << 63);

    //ArrayList<Integer>[] g;

    void solve() throws IOException {

        //Reader in = new Reader("in.txt");
        //out = new PrintWriter( new BufferedWriter(new FileWriter("output.txt")) );
        Reader in = new Reader();
        PrintWriter out = new PrintWriter( new BufferedWriter(new OutputStreamWriter(System.out)) );

        //BufferedReader br = new BufferedReader( new FileReader("in.txt") );
        //BufferedReader br = new BufferedReader( new InputStreamReader( System.in ) );

        //int n = in.nextInt();

        int[] z = new int[110];

        String s = in.nextLine();

        int cnt = 0;

        int c1 = 0;
        int c2 = 0;

        StringTokenizer tok = new StringTokenizer(s);

        int n = 0;

        while (tok.hasMoreElements()) {

            String t = tok.nextToken();

            if (t.equals("+")) {
                z[cnt++] = 1;
                c1++;
            }

            if (t.equals("-")) {
                z[cnt++] = 2;
                c2++;
            }

            if (!tok.hasMoreElements())
                n = Integer.valueOf(t);
        }

        if (cnt == 0) {

            System.out.println("Possible");
            System.out.println(n+" = "+n);
            return;
        }

        c1++;

        if (c1*n - c2 < n || c1 - c2*n > n) {

            System.out.println("Impossible");
            return;
        }

        int dif = n - (c1 - c2);

        int[] res = new int[cnt+1];
        Arrays.fill(res, 1);
        int pos = 0;

        while (dif > 0) {

            if (pos == 0 || z[pos-1] == 1) {

                res[pos] += Math.min(dif, n-1);
                dif -= Math.min(dif, n-1);
            }

            pos++;
        }

        while (dif < 0) {

            if (pos > 0 && z[pos-1] == 2) {

                res[pos] += Math.min(Math.abs(dif), n-1);
                dif += Math.min(Math.abs(dif), n-1);
            }

            pos++;
        }


        out.println("Possible");

        for (int i = 0; i < cnt+1; i++)
            if (i == 0)
                out.print(res[i]);
            else {
                out.print(z[i-1] == 1 ? " + " : " - ");
                out.print(res[i]);
            }

        out.print(" = ");
        out.print(n);

        out.flush();
        out.close();
    }

    long gcd(long a, long b) {

        if (b == 0)
            return a;

        return gcd(b, a%b);

    }


    class Item {

        int a;
        int b;
        int c;

        Item(int a, int b, int c) {
            this.a = a;
            this.b = b;
            this.c = c;
        }

    }

    class Pair implements Comparable<Pair>{

        int a;
        int b;
        int i;

        Pair(int a, int b, int i) {

            this.a = a;
            this.b = b;
            this.i = i;
        }

        public int compareTo(Pair p) {

            if (a > p.a)
                return 1;

            if (a < p.a)
                return -1;

            if (b > p.b)
                return 1;

            if (b < p.b)
                return -1;

            return 0;
        }

        //		@Override
        //		public boolean equals(Object o) {
        //			Pair p = (Pair) o;
        //			return a == p.a && b == p.b;
        //		}
        //
        //		@Override
        //		public int hashCode() {
        //			return Integer.valueOf(a).hashCode() + Integer.valueOf(b).hashCode();
        //		}

    }

    class Reader {

        BufferedReader  br;
        StringTokenizer tok;

        Reader(String file) throws IOException {
            br = new BufferedReader( new FileReader(file) );
        }

        Reader() throws IOException {
            br = new BufferedReader( new InputStreamReader(System.in) );
        }

        String next() throws IOException {

            while (tok == null || !tok.hasMoreElements())
                tok = new StringTokenizer(br.readLine());
            return tok.nextToken();
        }

        int nextInt() throws NumberFormatException, IOException {
            return Integer.valueOf(next());
        }

        long nextLong() throws NumberFormatException, IOException {
            return Long.valueOf(next());
        }

        double nextDouble() throws NumberFormatException, IOException {
            return Double.valueOf(next());
        }

        String nextLine() throws IOException {
            return br.readLine();
        }

    }

}