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

/**
 *
 * @author sarthak
 */
import java.util.*;
import java.math.*;
import java.io.*;

public class rnd347_B {

    static class FastScanner {

        BufferedReader br;
        StringTokenizer st;

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

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

        public String nextLine() {
            st = null;
            try {
                return br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
                return "";
            }
        }

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

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

        public double nextDouble() {
            return Double.parseDouble(next());
        }
    }

    public static int num(String ss) {
        int tbr = 0;
        for (int i = ss.length() - 1; i >= 0; i--) {
            tbr += (ss.charAt(i) - '0') * Math.pow(10, ss.length() - 1 - i);
        }
        return tbr;
    }

    public static String tostr(int n) {
        String tbr = "";
        while (n != 0) {
            tbr = "" + n % 10 + "" + tbr;
            n = n / 10;
        }
        return tbr;
    }

    static class P implements Comparable {

        private int x, y;

        public P(int x, int y) {
            this.x = x;
            this.y = y;
        }

        public int hashCode() {
            return (x * 31) ^ y;
        }

        public boolean equals(Object o) {
            if (o instanceof P) {
                P other = (P) o;
                return (x == other.x && y == other.y);
            }
            return false;
        }

        public int compareTo(Object obj) {
            P l = (P) obj;
            if (this.x == l.x) {
                if (this.y == l.y) {
                    return 0;
                }
                return (this.y < l.y) ? -1 : 1;
            }
            return (this.x < l.x) ? -1 : 1;
        }
    }

    public static void main(String[] args) {

        FastScanner s = new FastScanner(System.in);
        StringBuilder op = new StringBuilder();
        String ip = s.nextLine();
        char[] a=ip.toCharArray();
        int p=1;
        int n=0;
        for(char c:a)
        {
            if(c=='+')p++;
            if(c=='-')n++;
        }
        
     
        int N=num(ip.split(" ")[ip.split(" ").length-1]);
        if(!(N>=p-n*N && N<=p*N-n))
        {
            System.out.println("Impossible");
            return;
        }
        System.out.println("Possible");
        int cs=0;
        for(int i=0;i<a.length;i++)
        {
            if(a[i]=='=')
                break;
            if(!(a[i]=='?'))
            {
                op.append(a[i]);continue;
            }
            int sign=1;
            if(i>0&&a[i-2]=='-')sign=-1;
            if(sign==1)p--;
            if(sign==-1)n--;
          for(int j=1;j<=N;j++){
                if((cs+j*sign +p-n*N)<=N && N<=(cs+j*sign+p*N-n))
                {
                    op.append(j + "");
                    cs+=j*sign;
                    break;
                    
                }
            }
            
        }
        
        op.append("= " + N);
        System.out.println(op);
        
        
        
        
        
        
        
        
        
        
        
        
        
        
        
        
        
    }

}
