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

public class CF664F{

	private static InputStream stream;
	private static byte[] buf = new byte[1024];
	private static int curChar;
	private static int numChars;
	private static SpaceCharFilter filter;
	private static PrintWriter pw;
	

	private static void soln(){
		String str = nextLine();
		int l = str.length();
		int un=0,pl=1,min=0,kn=0;
		int i=0;
		while(i<l){
			if(str.charAt(i) == '?')
				un++;
			else if(str.charAt(i) == '+')
				pl++;
			else if(str.charAt(i) == '-')
				min++;
			else if(str.charAt(i) >= '0' && str.charAt(i) <= '9'){
				kn = Integer.parseInt(str.substring(i));
				break;
			}
			i++;
		}
		if(kn >= pl - min*kn && kn <= pl*kn - min){
			pw.println("Possible");
			int[] plus = new int[pl];
			int[] minus = new int[min];
			for (i=0; i<pl; i++) {
				plus[i]=1;
			}
			for (i=0; i<min; i++) {
				minus[i]=kn;
			}
			int temp = pl - min*kn;
			int x1 = 0 ;
			int x2 = 0 ;
			while(temp!=kn){
				if (kn == pl*kn - min){
					for (i=0; i<pl; i++) {
						plus[i]= kn;
					}
					for (i=0; i<min; i++) {
						minus[i]=1;
					}
					break;
				}
				else if(temp < kn){
					if(kn - temp > kn-1){
						if(x1<pl){
							plus[x1] = kn;
							temp = temp+(kn-1);
							x1++;
						}
						else{
							minus[x2] = 1;
							temp = temp+(kn-1);
							x2++;
						}
					}
					else{
						if(x1<pl){
							plus[x1] = kn - temp + 1;
							temp = kn;
							x1++;
						}
						else{
							minus[x2] = temp;
							temp = kn;
							x2++;
						}
					}
				}
			}
			x1 = 0;
			x2 = 0;
			i=0;
			while(i<l){
				if(str.charAt(i) == ' '){
					pw.print(' ');
				}
				else if(str.charAt(i) == '+'){
					pw.print("+");
				}
				else if(str.charAt(i) == '-'){
					pw.print("-");
				}
				else if(str.charAt(i) == '?'){
					if(i == 0){
						pw.print(plus[x1]);
						x1++;
					}
					else if (str.charAt(i-2) == '+'){
						pw.print(plus[x1]);
						x1++;
					}
					else if (str.charAt(i-2) == '-'){
						pw.print(minus[x2]);
						x2++;
					}
				}
				else if(str.charAt(i) == '='){
					pw.print('=');
				}
				else if(str.charAt(i) >= '0' && str.charAt(i) <= '9'){
					pw.println(kn);
					break;
				}
				i++;
			}			
		}
		else{
			pw.println("Impossible");
		}

	}

	public static void main(String[] args){
		InputReader(System.in);
		pw = new PrintWriter(System.out);
		soln();
		pw.close();
	}


	// To Get Input
	// Some Buffer Methods

	public static void InputReader(InputStream stream1) {
		stream = stream1;
	}

	private static boolean isWhitespace(int c) {
		return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
	}

	private static boolean isEndOfLine(int c) {
		return c == '\n' || c == '\r' || c == -1;
	}

	private static 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++];
	}

	private static int nextInt() {
		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;
	}
 
	private static long nextLong() {
		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;
	}
 
	private static String nextToken() {
		int c = read();
		while (isSpaceChar(c))
			c = read();
		StringBuilder res = new StringBuilder();
		do {
			res.appendCodePoint(c);
			c = read();
		} while (!isSpaceChar(c));
		return res.toString();
	}
 
	private static String nextLine() {
		int c = read();
		while (isSpaceChar(c))
			c = read();
		StringBuilder res = new StringBuilder();
		do {
			res.appendCodePoint(c);
			c = read();
		} while (!isEndOfLine(c));
		return res.toString();
	}

	private static int[] nextIntArray(int n) {
		int[] arr = new int[n];
		for (int i = 0; i < n; i++) {
			arr[i] = nextInt();
		}
		return arr;
	}
	  
	private static long[] nextLongArray(int n) {
		long[] arr = new long[n];
		for (int i = 0; i < n; i++) {
			arr[i] = nextLong();
		}
		return arr;
	}

	private static void pArray(int[] arr){
		for (int i=0; i<arr.length; i++) {
			System.out.print(arr[i] + " ");
		}
		System.out.println();
		return;
	}

	private static void pArray(long[] arr){
		for (int i=0; i<arr.length; i++) {
			System.out.print(arr[i] + " ");
		}
		System.out.println();
		return;		
	}

	private static boolean isSpaceChar(int c) {
		if (filter != null)
			return filter.isSpaceChar(c);
		return isWhitespace(c);
	}
 
	private interface SpaceCharFilter {
		public boolean isSpaceChar(int ch);
	}

}
