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.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Random;
import java.util.StringTokenizer;

public class Main {

	static class Pair implements Comparable<Pair> {

		int x;
		int y;

		Pair(int x, int y) {
			this.x = x;
			this.y = y;
		}

		@Override
		public int compareTo(Pair o) {
			int comp1 = Integer.compare(x, o.x);
			if (comp1 != 0) {
				return comp1;
			}
			return Integer.compare(y, o.y);
		}

	}

	static int MOD = 1000 * 1000 * 1000 + 7;

	public static void shuffleArray(int[] arr) {
		int n = arr.length;
		Random rnd = new Random();
		for (int i = 0; i < n; ++i) {
			int tmp = arr[i];
			int randomPos = i + rnd.nextInt(n - i);
			arr[i] = arr[randomPos];
			arr[randomPos] = tmp;
		}
	}

	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		InputReader in = new InputReader(inputStream);
		PrintWriter out = new PrintWriter(outputStream);
		solve(in, out);
		out.close();
		System.exit(0);
	}

	private static void solve(InputReader in, PrintWriter out) {
		String a = in.nextLine();
		if (a.charAt(0) != '-') {
			a = "+" + a;
		}

		ArrayList<Integer> ar = new ArrayList<>();
		int eqPos = a.indexOf('=');
		int plus = 0;
		int minus = 0;
		for (int i = 2; i < a.length(); i++) {
			if (a.charAt(i - 2) == '+') {
				ar.add(1);
				plus++;
			} else if (a.charAt(i - 2) == '-') {
				ar.add(-1);
				minus++;
			}
		}

		String nStr = a.substring(eqPos + 2);
		int n = Integer.parseInt(nStr);
		int N = n;
		int k = ar.size();
		int[] tab = new int[k];
		n -= plus;
		n += minus;

		for (int i = 0; i < k; i++) {
			if (n > 0 && ar.get(i) > 0) {
				tab[i] += Math.min(n, N - 1);
				n -= tab[i];
			} else if (n < 0 && ar.get(i) < 0) {
				tab[i] += Math.min(-n, N - 1);
				n += tab[i];
			}
		}
		//
		// for (int i = 0; i < k; i++) {
		// if (n > 0 && ar.get(i) < 0) {
		// tab[i] += Math.min(n, N - 1);
		// n -= tab[i];
		// } else if (n < 0 && ar.get(i) > 0) {
		// tab[i] += Math.min(n, N - 1);
		// n += tab[i];
		// }
		// }

		int pos = 0;
		if (a.charAt(0) == '+') {
			a = a.substring(1);
		}
		if (n == 0) {
			out.println("Possible");
			for (int i = 0; i < a.length(); i++) {
				if (a.charAt(i) == '?') {
					out.print(tab[pos++] + 1);
				} else {
					out.print(a.charAt(i));
				}
			}
		} else {
			out.print("Impossible");
		}

	}

	/*
		* 
		*/
	// --------------------------------------------------------

	private static int gcd(int n, int m) {
		if (m == 0) {
			return n;
		}

		return gcd(m, n % m);
	}

	static class InputReader {
		public BufferedReader reader;
		public StringTokenizer tokenizer;

		public InputReader(InputStream stream) {
			reader = new BufferedReader(new InputStreamReader(stream), 32768);
			tokenizer = null;
		}

		public String next() {
			while (tokenizer == null || !tokenizer.hasMoreTokens()) {
				try {
					tokenizer = new StringTokenizer(reader.readLine());
				} catch (IOException e) {
					throw new RuntimeException(e);
				}
			}
			return tokenizer.nextToken();
		}

		public int nextInt() {
			return Integer.parseInt(next());
		}

		public long nextLong() {
			return Long.parseLong(next());
		}

		public double nextDouble() {
			return Double.parseDouble(next());
		}

		public String nextLine() {
			String str = "";
			try {
				str = reader.readLine();
			} catch (IOException e) {
				e.printStackTrace();
			}

			return str;
		}
	}

}