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
//package ap;

import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.InputMismatchException;



public class Main {

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		InputReader scnr = new InputReader(System.in);
		PrintWriter out = new PrintWriter(System.out);
//int n=scnr.nextInt();
char ar[]=new char[10000];

int i=0;
int p=1;
int s=0;
while(true){
	String st=scnr.readString();

	if(st.equals("=")){
		break;
	}
	if(st.equals("-")){
			s++;
	}
	if(st.equals("+")){
		p++;		
	}
	ar[i]=st.charAt(0);
	i++;
}

int n=scnr.nextInt();
//System.out.println(p+" "+s);
int max=n*p-1*s;
int min=1*p-n*s;
if(n>max){
	System.out.println("Impossible");
	return ;
}
if(n<min){
System.out.println("Impossible");	
return ;
}
double x=n/(p*1.0);
double val=x+(s*1)/(p*1.0);
int b=1;
int cl=0;
while(!(1<=val&&val<=n)){
	b++;
val=x+(s*b)/(p*1.0);
}
int tot=n+b*s;
int plus[]=new int[p];
int va=tot/p;
//System.out.println(tot);
for(int mo=0;mo<p;mo++){
	plus[mo]=va;
}
for(int mo=0;mo<tot%p;mo++){
	plus[mo]++;
}
out.println("Possible");
int pu=0;
out.print(plus[pu]+" ");
pu++;
for(int y=1;y<2*(p+s)-1;y++){
	if(ar[y]=='+'){
		out.print("+"+" "+plus[pu]+" ");
		pu++;
		y++;
	}
	else{
		out.print("-"+" "+b+" ");
		y++;
	}
}
out.print("="+" ");
out.print(n);
out.println();
	




	out.close();
	}


	static class pair implements Comparable<pair> {
		int val;
		int index;

		@Override
		public int compareTo(pair arg0) {
			// TODO Auto-generated method stub
			return -1 * (this.val - arg0.val);
		}
	}

	static class InputReader {

		private final InputStream stream;
		private final byte[] buf = new byte[8192];
		private int curChar, snumChars;

		public InputReader(InputStream st) {
			this.stream = st;
		}

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

		public int nextInt() {
			int c = read();
			while (isSpaceChar(c)) {
				c = read();
			}
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			int res = 0;
			do {
				res *= 10;
				res += c - '0';
				c = read();
			} while (!isSpaceChar(c));
			return res * sgn;
		}

		public long nextLong() {
			int c = read();
			while (isSpaceChar(c)) {
				c = read();
			}
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			long res = 0;
			do {
				res *= 10;
				res += c - '0';
				c = read();
			} while (!isSpaceChar(c));
			return res * sgn;
		}

		public int[] nextIntArray(int n) {
			int a[] = new int[n];
			for (int i = 0; i < n; i++) {
				a[i] = nextInt();
			}
			return a;
		}

		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 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();
		}

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

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

	}

}

