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.BufferedReader;
import java.io.BufferedWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.HashMap;
import java.util.Map;
import java.util.Map.Entry;
import java.util.Set;
import java.util.StringTokenizer;
import java.util.TreeMap;
import java.util.TreeSet;

public class C347B {

	static StringTokenizer st;
	static BufferedReader br;
	static PrintWriter pw;
	static int[] vplus = new int [101];
	static int[] vminus = new int [101];
	static int lp = 0, lm = 0;
	public static void main(String[] args) throws IOException {
		br = new BufferedReader(new InputStreamReader(System.in));
		pw = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
		int plus = 1;
		int minus = 0;
		boolean[] znak = new boolean [101];
		int len = 0;
		next();
		String sign = next();
		while (!sign.equals("=")) {
			if (sign.equals("+")) {
				plus++;
				len++;
			} else {
				minus++;
				znak[len++] = true;
			}
			next();
			sign = next();
		}
		int n = nextInt();
		//System.out.println(plus + " " + minus + " " + n);
		if (plus == 1) {
			if (minus > 0) {
				pw.println("Impossible");
			} else {
				pw.println("Possible");
				pw.println(n + " = " + n);
			}
		} else {
			if ((plus * n - minus < n) || (plus - n * minus > n))
				pw.println("Impossible");
			else {
				find(plus, minus, n, n);
				pw.println("Possible");
				int curp = 0, curm = 0;
				pw.print(vplus[curp++]);
				for (int i = 0; i < len; ++i) 
					if (!znak[i]) {
						pw.print(" + " + vplus[curp++]);
					} else {
						pw.print(" - " + vminus[curm++]);
					}
				pw.println(" = " + n);
			}
		}
		pw.close();
	}
	
	private static void find(int plus, int minus, int n, int ans) {
		if (plus + minus == 0)
			return;
		if (plus == 0) {
			//System.out.println(minus + "  " + ans);
			if ((minus - 1) * n >= -ans) {
				vminus[lm++] = 1;
				find(plus, minus - 1, n, ans + 1);
			} else {
				if (n * minus >= -ans && (-ans - n + (minus - 1) * n > 0)) {
					vminus[lm++] = n;
					find(plus, minus - 1, n, ans + n);
				} else {
					if (minus == 1) {
						vminus[lm++] = -ans;
						return;
					} else {
						int a = 1 / 0;
					}
				}
			}
		} else if (check(plus - 1, minus, n, ans - 1)) {
			vplus[lp++] = 1;
			find(plus - 1, minus, n, ans - 1);
		} else if (check(plus - 1, minus, n, ans - n)) {
			//System.out.print(plus + " " + minus + " " + ans);
			vplus[lp++] = n;
			find(plus - 1, minus, n, ans - n);
		} else {
			if (plus == 1) {
				for (int i = 1; i <= n; ++i) {
					if (check(0, minus, n, ans - i)) {
						vplus[lp++] = i;
						find(0, minus, n, ans - i);
						return;
					}
				}
			} else {
				//System.out.println(plus + " " + minus + " " + ans);
				int a = 1 / 0;
			}
		}
		
	}

	private static boolean check(int plus, int minus, int n, int ans) {
		boolean answ1 = plus * n - minus >= ans;
		boolean answ2 = plus - minus * n <= ans;
		return answ1 && answ2;
	}

	private static int sumf(int[] fen, int id) {
		int summ = 0;
		for (; id >= 0; id = (id & (id + 1)) - 1) 
 			summ += fen[id];
		return summ;
	}

	private static void addf(int[] fen, int id) {
		for (; id < fen.length; id |= id + 1) 
			fen[id]++;
	}

	private static int nextInt() throws IOException {
		return Integer.parseInt(next());
	}
	private static long nextLong() throws IOException {
		return Long.parseLong(next());
	}
	private static double nextDouble() throws IOException {
		return Double.parseDouble(next());
	}
	private static String next() throws IOException {
		while (st==null || !st.hasMoreTokens())
			st = new StringTokenizer(br.readLine());
		return st.nextToken();
	}
}