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.BufferedOutputStream;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class Rebus {

    /**
     * Scanner class
     *
     * @author gouthamvidyapradhan
     */
    static class MyScanner {
        /**
         * Buffered reader
         */
        private static BufferedReader br = new BufferedReader(
                new InputStreamReader(System.in));

        private static StringTokenizer st;

        /**
         * Read integer
         *
         * @return
         * @throws Exception
         */
        public static int readInt() throws Exception {
            try {
                if (st != null && st.hasMoreTokens()) {
                    return parseInt(st.nextToken());
                }
                String str = br.readLine();
                if (str != null && !str.trim().equals("")) {
                    st = new StringTokenizer(str);
                    return parseInt(st.nextToken());
                }
            } catch (IOException e) {
                close();
                return -1;
            }
            return -1;
        }

        /**
         * Read integer
         *
         * @return
         * @throws Exception
         */
        public static long readLong() throws Exception {
            try {
                if (st != null && st.hasMoreTokens()) {
                    return Long.parseLong(st.nextToken());
                }
                String str = br.readLine();
                if (str != null && !str.trim().equals("")) {
                    st = new StringTokenizer(str);
                    return Long.parseLong(st.nextToken());
                }
            } catch (IOException e) {
                close();
                return -1;
            }
            return -1;
        }

        /**
         * Read line
         * @return
         * @throws Exception
         */
        public static String readLine() throws Exception
        {
            return br.readLine();
        }

        /**
         * Parse to integer
         * @param in
         * @return integer value
         */
        public static int parseInt(String in)
        {
            // Check for a sign.
            int num  = 0, sign = -1, i = 0;
            final int len  = in.length( );
            final char ch  = in.charAt( 0 );
            if ( ch == '-' )
                sign = 1;
            else
                num = '0' - ch;

            // Build the number.
            i+=1;
            while ( i < len )
                num = num*10 + '0' - in.charAt( i++ );
            return sign * num;
        }

        /**
         * Close BufferedReader
         *
         * @throws Exception
         */
        public static void close() throws Exception {
            br.close();
        }
    }

    private static PrintWriter pw = new PrintWriter(new BufferedOutputStream(System.out, 1000000));
    private static int N;
    private static String line, lhs;
    private static int[] P, M;
    private static final String PLUS = "+", MINUS = "-", 
    		BLANK = " ", EQUAL = "=", POSSIBLE = "Possible", IMPOSSIBLE = "Impossible";
    /**
     * Main method
     * @param args
     */
	public static void main(String[] args) throws Exception 
	{
		line = MyScanner.readLine().trim();
		StringTokenizer st = new StringTokenizer(line, EQUAL);
		lhs = st.nextToken().trim();
		N = MyScanner.parseInt(st.nextToken().trim());
		int l = lhs.length();
		int plus = 1, minus = 0, sum = 0;
		boolean done = false;
		for(int i = 0; i < l; i++)
		{
			switch (lhs.charAt(i)) 
			{
				case '+':
					plus++;
					break;
	
				case '-':
					minus++;
					break;
					
				default:
					break;
			}
		}
		P = new int[plus];
		M = new int[minus];
		int max = (N * plus) - minus;
		int min = (N * minus * -1) + plus;
		if(N > max || N < min)
			pw.println(IMPOSSIBLE);
		else
		{
			for(int i = 0, le = P.length; i < le; i++)
			{
				P[i] = 1;
				sum += 1;
			}
			for(int i = 0, le = M.length; i < le; i++)
			{
				M[i] = 1;
				sum -= 1;
			}
			if(sum < N) //need increment
			{
				for(int i = 0, le = P.length; i < le && !done; i++)
				{
					int temp = (sum - P[i]) + N;
					if(temp == N)
					{
						P[i] = N;
						sum = temp;
						done = true;
						break;
					}
					else if(temp < N)
					{
						P[i] = N;
						sum = temp;
					}
					else
					{
						for(int j = 1; j <= N; j++)
						{
							temp = (sum - P[i]) + j;
							if(temp == N)
							{
								sum = temp;
								P[i] = j;
								done = true;
								break;
							}
						}
					}
				}
			}
			else if(sum > N)
			{
				for(int i = 0, le = M.length; i < le && !done; i++)
				{
					int temp = (sum + M[i]) - N;
					if(temp == N)
					{
						M[i] = N;
						sum = temp;
						done = true;
						break;
					}
					else if(temp > N)
					{
						M[i] = N;
						sum = temp;
					}
					else
					{
						for(int j = 1; j <= N; j++)
						{
							temp = (sum + M[i]) - j;
							if(temp == N)
							{
								sum = temp;
								M[i] = j;
								done = true;
								break;
							}
						}
					}
				}
			}
			print();
		}
		pw.flush(); pw.close(); MyScanner.close();
	}
	
	/**
	 * Print values
	 */
	private static void print()
	{
		pw.println(POSSIBLE);
		line = line.replaceFirst("\\?", String.valueOf(P[0]));
		for(int i = 1, l = P.length; i < l; i++)
			line = line.replaceFirst("\\+ \\?", PLUS + BLANK + String.valueOf(P[i]));
		for(int i = 0, l = M.length; i < l; i++)
			line = line.replaceFirst("\\- \\?", MINUS + BLANK + String.valueOf(M[i]));
		pw.println(line);
	}
}
