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
/*
 * PDPM IIITDM Jabalpur
 * Asutosh Rana
 */

import java.util.*;
import java.io.*;
import java.math.*;

public class Main
{
    static long MOD = 1000000007;
    public static void main (String[] args) throws java.lang.Exception
    {
        InputReader in=new InputReader(System.in);
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter out=new PrintWriter(System.out);

        int t = 1;//in.readInt();

        while(t-->0){
            char[] S = br.readLine().toCharArray();
            int count0 = 1,count1 =0,rev = 0,n = 0;
            int j=S.length-1;
            	while(Character.isDigit(S[j])){
            		rev = rev*10 + (S[j]-'0');
            		j--;
            	}
            	//out.println(rev);
            	while(j<S.length-1){
            		n = n*10 + (rev%10);
            		rev/=10;j++;
            	}
            //out.println(n);
            for(int i=0;i<S.length;i++)
            	if(S[i]=='+'){
            		count0++;
            	}
            	else if(S[i]=='-'){
            		count1++;
            	}
            if(count0*n-count1<n)
            	out.println("Impossible");
            else if(count0-count1*n > n)
            	out.println("Impossible");
            else{
            	out.println("Possible");
            	int req = n - count0 + count1;
            	//out.println(req+ " "+count0+" "+count1);
            	if(req>=n-1){
            		out.print(n);
            		req -= (n-1);
            	}
            	else if(req>0){
            		out.print(req+1);
            		req=0;
            	}
            	else{
            		out.print("1");
            	}
            	for(int i=1;i<S.length;i++){
            		if(S[i]=='?' && S[i-2]=='-'){
            			if(req<0-(n-1)){
                    		out.print(n);
                    		req +=(n-1);
            			}
                    	else if(req<0){
                    		out.print(0-req+1);
                    		req=0;
                    	}
                    	else{
                    		out.print("1");
                    	}
            		}
            		else if(S[i]=='?' && S[i-2]=='+'){
            			if(req>=n-1){
                    		out.print(n);
                    		req-=(n-1);
            			}
                    	else if(req>0){
                    		out.print(req+1);
                    		req=0;
                    	}
                    	else{
                    		out.print("1");
                    	}
            		}	
            		else
            			out.print(S[i]);
            	}
            	out.println();
            }
        }
        out.flush();
        out.close();
    }


}

class InputReader{
    private InputStream stream;
    private byte[] buf = new byte[1024];
    private int curChar;
    private int numChars;
    private SpaceCharFilter filter;

    public InputReader(InputStream stream){this.stream = stream;}
    public int read(){
        if (numChars==-1) throw new InputMismatchException();
        if (curChar >= numChars){
            curChar = 0;
            try {numChars = stream.read(buf);}
            catch (IOException e){throw new InputMismatchException();}
            if(numChars <= 0) return -1;
        }
        return buf[curChar++];
    }

    public int readInt(){
        int c = read();
        while(isSpaceChar(c)) c = read();
        int sgn = 1;
        if (c == '-') {sgn = -1;c = read();}
        int res = 0;
        do {
            if(c<'0'||c>'9') throw new InputMismatchException();
            res *= 10;
            res += c - '0';
            c = read();
        }
        while (!isSpaceChar(c)); return res * sgn;
    }

    public void readInt(int[] A){
        for(int i=0;i<A.length;i++)
            A[i] = readInt();
    }

    public long readLong() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = read();
        }
        long res = 0;
        do {
            if (c < '0' || c > '9')
                throw new InputMismatchException();
            res *= 10;
            res += c - '0';
            c = read();
        }
        while (!isSpaceChar(c));
        return res * sgn;
    }

    public void readLong(long[] A){
        for(int i=0;i<A.length;i++)
            A[i] = readLong();
    }

    public double readDouble() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = read();
        }
        double res = 0;
        while (!isSpaceChar(c) && c != '.') {
            if (c == 'e' || c == 'E')
                return res * Math.pow(10, readInt());
            if (c < '0' || c > '9')
                throw new InputMismatchException();
            res *= 10;
            res += c - '0';
            c = read();
        }
        if (c == '.') {
            c = read();
            double m = 1;
            while (!isSpaceChar(c)) {
                if (c == 'e' || c == 'E')
                    return res * Math.pow(10, readInt());
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                m /= 10;
                res += (c - '0') * m;
                c = read();
            }
        }
        return res * sgn;
    }

    public char[] readCharA(){
        return readString().toCharArray();
    }

    public String readString() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        StringBuilder res = new StringBuilder();
        do {
            res.appendCodePoint(c);
            c = read();
        } while (!isSpaceChar(c));
        return res.toString();
    }

    public boolean isSpaceChar(int c) {
        if (filter != null)
            return filter.isSpaceChar(c);
        return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
    }

    public String next() {
        return readString();
    }

    public interface SpaceCharFilter {
        public boolean isSpaceChar(int ch);
    }

}