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 com.sun.org.apache.xml.internal.utils.StringComparable;

import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.text.DecimalFormat;
import java.text.NumberFormat;
import java.util.*;

public class Main {
    public static void main(String[] args) {
//     Test.testing();
        ConsoleIO io = new ConsoleIO();
        new Main(io).solve();
        io.close();
    }

    ConsoleIO io;

    Main(ConsoleIO io) {
        this.io = io;
    }

    ArrayList<ArrayList<Integer>> gr;
    boolean[] visit;

    class Edge {
        public Edge(int u, int v, int c) {
            this.u = u;
            this.v = v;
            this.c = c;
        }

        public int u;
        public int v;
        public int c;
    }

    long MOD = 1_000_000_007;
    int N, M;
    long K;
    double[][] map;

    public void solve() {
        char[] s = io.readLine().toCharArray();
        int pos = 1;
        int neg = 0;
        int n = 0;
        for (int i = 0; i < s.length; i++) {
            if (s[i] == '+')
                pos++;
            if (s[i] == '-')
                neg++;
            if (s[i] == '=') {
                n = Integer.parseInt(new String(s, i + 1, s.length - i - 1).trim());
            }
        }
        int lim = n;
        int min = (pos) - neg * n;
        int max = (pos) * n - neg;
        if (min > n || max < n) {
            io.writeLine("Impossible");
        } else {
            io.writeLine("Possible");
            StringBuilder sb = new StringBuilder();
            boolean p = true;
            for (int i = 0; i < s.length; i++) {
                if (s[i] == '?') {
                    if (p) {
                        if (pos + neg == 1) {
                            sb.append(n);
                        } else {
                            int tmax = (pos - 1) * lim - neg;
                            if (tmax < n) {
                                int t = Math.min(lim, n - tmax);
                                sb.append(t);
                                n -= t;
                            } else {
                                sb.append("1");
                                n -= 1;
                            }
                        }
                        pos--;
                    } else {
                        if (pos + neg == 1) {
                            sb.append(-n);
                        } else {
                            int tmin = (pos) - (neg - 1) * lim;
                            if (tmin > n) {
                                int t = Math.min(lim, tmin - n);
                                sb.append(t);
                                n += t;
                            } else {
                                sb.append("1");
                                n += 1;
                            }
                        }
                        neg--;
                    }
                } else {
                    if (s[i] == '-') p = false;
                    if (s[i] == '+') p = true;
                    sb.append(s[i]);
                }
            }
            io.writeLine(sb.toString());
        }
    }

    long gcd(long a, long b) {
        if (a < b) return gcd(b, a);
        if (b == 0) return a;
        return gcd(b, a % b);
    }
}

class ConsoleIO {
    BufferedReader br;
    PrintWriter out;
    public ConsoleIO(){br = new BufferedReader(new InputStreamReader(System.in));out = new PrintWriter(System.out);}
    public void flush(){this.out.flush();}
    public void close(){this.out.close();}
    public void writeLine(String s) {this.out.println(s);}
    public void writeInt(int a) {this.out.print(a);this.out.print(' ');}
    public void writeWord(String s){
        this.out.print(s);
    }
    public int read(char[] buf, int len){try {return br.read(buf,0,len);}catch (Exception ex){ return -1; }}
    public String readLine() {try {return br.readLine();}catch (Exception ex){ return "";}}
    public long[] readLongArray() {
        String[]n=this.readLine().trim().split("\\s+");long[]r=new long[n.length];
        for(int i=0;i<n.length;i++)r[i]=Long.parseLong(n[i]);
        return r;
    }
    public int[] readIntArray() {
        String[]n=this.readLine().trim().split("\\s+");int[]r=new int[n.length];
        for(int i=0;i<n.length;i++)r[i]=Integer.parseInt(n[i]);
        return r;
    }
    public int[] readIntArray(int n) {
        int[] res = new int[n];
        char[] all = this.readLine().toCharArray();
        int cur = 0;boolean have = false;
        int k = 0;
        boolean neg = false;
        for(int i = 0;i<all.length;i++){
            if(all[i]>='0' && all[i]<='9'){
                cur = cur*10+all[i]-'0';
                have = true;
            }else if(all[i]=='-') {
                neg = true;
            }
            else if(have){
                res[k++] = neg?-cur:cur;
                cur = 0;
                have = false;
                neg = false;
            }
        }
        if(have)res[k++] = neg?-cur:cur;
        return res;
    }
    public int readInt() {
        try {
            int r = 0;
            boolean start = false;
            boolean neg = false;
            while (true) {
                int c = br.read();
                if (c >= '0' && c <= '9') {
                    r = r * 10 + c - '0';
                    start = true;
                } else if (!start && c == '-') {
                    start = true;
                    neg = true;
                } else if (start || c == -1) return neg ? -r : r;
            }
        } catch (Exception ex) {
            return -1;
        }
    }
    public long readLong() {
        try {
            long r = 0;
            boolean start = false;
            boolean neg = false;
            while (true) {
                int c = br.read();
                if (c >= '0' && c <= '9') {
                    r = r * 10 + c - '0';
                    start = true;
                } else if (!start && c == '-') {
                    start = true;
                    neg = true;
                } else if (start || c == -1) return neg ? -r : r;
            }
        } catch (Exception ex) {
            return -1;
        }
    }
    public String readWord() {
        try {
            boolean start = false;
            StringBuilder sb = new StringBuilder();
            while (true) {
                int c = br.read();
                if (c!= ' ' && c!= '\r' && c!='\n' && c!='\t') {
                    sb.append((char)c);
                    start = true;
                } else if (start || c == -1) return sb.toString();
            }
        } catch (Exception ex) {
            return "";
        }
    }
    public void writeIntArray(int[] a) {
        StringBuilder sb = new StringBuilder();
        for (int i = 0; i < a.length; i++) {if (i > 0) sb.append(' ');sb.append(a[i]);}
        this.writeLine(sb.toString());
    }
}
class Pair {
    public Pair(int a, int b) {this.a = a;this.b = b;}
    public int a;
    public int b;
}
class Tri {
    public Tri(int a, int b, int c) {this.a = a;this.b = b;this.c = c;}
    public int a;
    public int b;
    public int c;
}
class PairLL {
    public PairLL(long a, long b) {this.a = a;this.b = b;}
    public long a;
    public long b;
}



