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.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.NoSuchElementException;
 
import java.util.*;
public class Main {
	Scanner cin = new Scanner(System.in);
	String s;
	int S,N;
	int[] ans,op;
	ArrayList<Integer> plist,mlist;
	public boolean dfs(int n,int sum){
		if(n == N){
			return sum == S;
		}
		
		for(int i = 1;i<=S;i++){
			boolean ret;
			if(op[n] == 0)ret = dfs(n + 1,sum + i);
			else ret = dfs(n + 1,sum - i);
			
			if(ret){
				ans[n] = i;
				return true;
			}
		}
		return false;
	}
	public void solve(){
		s = cin.nextLine();
		S = Integer.parseInt(s.substring(s.indexOf("=") + 2));
		int plus = 1;
		int minus = 0;
		for(int i = 0;i < s.length();i++){
			if(s.charAt(i) == '+')plus++;
			else if(s.charAt(i) == '-')minus++;
		}
		
		N = plus + minus;
		ans = new int[N];
		op = new int[N];
		int it = 0;
		op[it] = 0;
		it = 1;
		for(int i = 0;i < s.length();i++){
			if(s.charAt(i) == '+'){
				op[it] = 0;
				it++;
			}else if(s.charAt(i) == '-'){
				op[it] = 1;
				it++;
			}
		}
		if(plus == 1 && minus == 0){
			out.println("Possible");
			out.println(S + " = " + S);
			return;
		}
		else if(plus <= minus){
			int plusSum = (plus  - 1)* S;
			int minusCnt = 0;
			ans[0] = S;
			for(int i = 1;i < N;i++){
				if(op[i] == 1){
					int m = minus - minusCnt - 1;
					if(plusSum <= m){
						out.println("Impossible");
						return;
					}
					
					ans[i] = Math.min(S,plusSum - m);
					plusSum -= ans[i];
					minusCnt++;
				}else{
					ans[i] = S;
				}
			}
		}else if(plus > minus){
			int minusSum = minus * S + (S - 1);
			int plusCnt = 1;
			ans[0] = 1;
			for(int i = 1;i < N;i++){
				if(op[i] == 0){
					int p = plus - plusCnt - 1;
					if(minusSum <= p){
						out.println("Impossible");
						return;
					}
					ans[i] = Math.min(S,minusSum - p);
					minusSum -= ans[i];
					plusCnt++;
				}else{
					ans[i] = S;
				}
			}
		}
		
		out.println("Possible");
		out.print(ans[0]);
		for(int i = 1;i < N;i++){
			out.print(" " + (op[i] == 0 ? "+ " : "- ") + ans[i]);
		}
		out.println(" = " + S);
	}
 
	public static void main(String[] args) {
		out.flush();
		new Main().solve();
		out.close();
	}
 
	/* Input */
	private static final InputStream in = System.in;
	private static final PrintWriter out = new PrintWriter(System.out);
	private final byte[] buffer = new byte[2048];
	private int p = 0;
	private int buflen = 0;
 
	private boolean hasNextByte() {
		if (p < buflen)
			return true;
		p = 0;
		try {
			buflen = in.read(buffer);
		} catch (IOException e) {
			e.printStackTrace();
		}
		if (buflen <= 0)
			return false;
		return true;
	}
 
	public boolean hasNext() {
		while (hasNextByte() && !isPrint(buffer[p])) {
			p++;
		}
		return hasNextByte();
	}
 
	private boolean isPrint(int ch) {
		if (ch >= '!' && ch <= '~')
			return true;
		return false;
	}
 
	private int nextByte() {
		if (!hasNextByte())
			return -1;
		return buffer[p++];
	}
 
	public String next() {
		if (!hasNext())
			throw new NoSuchElementException();
		StringBuilder sb = new StringBuilder();
		int b = -1;
		while (isPrint((b = nextByte()))) {
			sb.appendCodePoint(b);
		}
		return sb.toString();
	}
 
	public int nextInt() {
		return Integer.parseInt(next());
	}
 
	public long nextLong() {
		return Long.parseLong(next());
	}
 
	public double nextDouble() {
		return Double.parseDouble(next());
	}
}