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.PrintWriter;
import java.util.Arrays;

public class CF2_347B {
  
  static Reader sc = new Reader();
  static PrintWriter out = new PrintWriter(System.out);
  
  public static void main(String[] args) throws IOException {
    String[] words = sc.nextLine().split(" ");
    int n = Integer.parseInt(words[words.length - 1]);
    int count = (words.length - 1) / 2;
    int[] nums = new int[count];
    boolean[] neg = new boolean[count];
    
    for (int i = 1; i < count; i++) {
      if (words[i * 2 - 1].charAt(0) != '+') {
        neg[i] = true;
      }
    }
    
    int sum = 0;
    for (int i = 0; i < count; i++) {
      nums[i] = 1;
      sum += neg[i] ? - nums[i] : +nums[i];
    }
    
    int maxed = 0;
    
    
    if (sum < n) {
      for (int i = 0; i < count; i++) {
        if (!neg[i]) {
          int canAdd = Math.min(n - sum, n - nums[i]);
          nums[i] += canAdd;
          sum += canAdd;
        }
      }
    } else if (sum > n) {
      for (int i = 0; i < count; i++) {
        if (neg[i]) {
          int canSub = Math.min(sum - n, n - nums[i]);
          nums[i] += canSub;
          sum -= canSub;
        }
      }
    }
    
    if (sum == n) {
      out.println("Possible");
      for (int i = 0; i < count; i++) {
        if (i != 0) {
          if (neg[i]) {
            out.print("- ");
          } else {
            out.print("+ ");
          }
        }
        out.print(nums[i] + " ");
      }
      
      out.println("= " + n);
    } else {
      out.println("Impossible");
    }
    
    
    out.close();
  }
  
  
  
  static class Reader {
    boolean consume = false; final private int BUFFER_SIZE = 1 << 12;private byte[] buffer;private int bufferPointer, bytesRead;private boolean reachedEnd = false;public Reader() {buffer = new byte[BUFFER_SIZE];bufferPointer = 0;bytesRead = 0;}
    public boolean hasNext() {return !reachedEnd;} private void fillBuffer() throws IOException {bytesRead = System.in.read(buffer, bufferPointer = 0, BUFFER_SIZE);if (bytesRead == -1) {buffer[0] = -1;reachedEnd = true;}}
    private void consumeSpaces() throws IOException {while (read() <= ' ' && reachedEnd == false);bufferPointer--;} private byte read() throws IOException {if (bufferPointer == bytesRead) {fillBuffer();}return buffer[bufferPointer++];}
    public String next() throws IOException {StringBuilder sb = new StringBuilder();consumeSpaces();byte c = read();do {sb.append((char) c);} while ((c = read()) > ' ');if (consume) {consumeSpaces();};if (sb.length() == 0) {return null;}return sb.toString();}
    public String nextLine() throws IOException {StringBuilder sb = new StringBuilder();byte c;boolean read = false;while ((c = read()) != -1) {if (c == '\n') {read = true;break;}if (c >= ' ')sb.append((char) c);}if (!read) {return null;}return sb.toString();}
    public int nextInt() throws IOException {consumeSpaces();int ret = 0;      byte c = read();boolean neg = (c == '-');if (neg) {c = read();}do {ret = ret * 10 + c - '0';} while ((c = read()) >= '0' && c <= '9');if (consume) {consumeSpaces();}if (neg) {return -ret;}return ret;}
    public long nextLong() throws IOException {consumeSpaces();long ret = 0;byte c = read();boolean neg = (c == '-');if (neg) {c = read();}do {ret = ret * 10L + c - '0';} while ((c = read()) >= '0' && c <= '9');if (consume) {consumeSpaces();}if (neg) {return -ret;}return ret;}
    public double nextDouble() throws IOException {consumeSpaces();double ret = 0;double div = 1;byte c = read();boolean neg = (c == '-');if (neg) {c = read();}do {ret = ret * 10 + c - '0';} while ((c = read()) >= '0' && c <= '9');if (c == '.') {while ((c = read()) >= '0' && c <= '9') {ret += (c - '0') / (div *= 10);}}if (consume) {consumeSpaces();}if (neg) {return -ret;}return ret;}    public int[] nextIntArray(int n) throws IOException {int[] a = new int[n];for (int i = 0; i < n; i++) {a[i] = nextInt();}return a;}
    public int[][] nextIntMatrix(int n, int m) throws IOException {int[][] grid = new int[n][m];for (int i = 0; i < n; i++) {grid[i] = nextIntArray(m);}return grid;}
    public char[][] nextCharacterMatrix(int n) throws IOException {char[][] a = new char[n][];for (int i = 0; i < n; i++) {a[i] = next().toCharArray();}return a;}
    public void close() throws IOException {if (System.in == null) {return;} else {System.in.close();}}
  }
  
  static void print(int[] A) {for (int i = 0; i < A.length; i++) {if (i != 0) {out.print(' ');}out.print(A[i]);}out.println();}
  static <T> void print(Iterable<T> A) {int i = 0;for (T act : A) {if (i != 0) {out.print(' ');}out.print(act);i++;}out.println();}
  static void printPlus1(Iterable<Number> A) {int i = 0;for (Number act : A) {if (i != 0) {out.print(' ');}out.print(act.longValue() + 1L);i++;}out.println();  }
  static void debug(Object... o) {System.err.println(Arrays.deepToString(o));}
  
  /*
  long s = System.currentTimeMillis();
  debug(System.currentTimeMillis() - s + "ms");
   */
}
