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.File;
import java.io.FileInputStream;
import java.io.FileNotFoundException;
import java.io.FileOutputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.BitSet;
import java.util.Calendar;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.LinkedList;
import java.util.PriorityQueue;
import java.util.SortedSet;
import java.util.Stack;
import java.util.StringTokenizer;
import java.util.TreeMap;
import java.util.TreeSet;

/**
 * #
 * @author pttrung
 */
public class B_Round_347_Div2 {

    public static long MOD = 1000000007;

    public static void main(String[] args) throws FileNotFoundException {
        // PrintWriter out = new PrintWriter(new FileOutputStream(new File(
        // "output.txt")));
        PrintWriter out = new PrintWriter(System.out);
        Scanner in = new Scanner();
        String[] tmp = in.nextLine().split(" ");
        int n = Integer.parseInt(tmp[tmp.length - 1]);
        int cur = 0;
        int neg = 0;
        int pos = 0;
        for (int i = 0; i < tmp.length - 2; i += 2) {
            if (i > 0) {

                if (tmp[i].equals("?")) {
                    if (tmp[i - 1].equals("-")) {
                        neg++;
                    } else {
                        pos++;
                    }
                } else if (tmp[i - 1].equals("+")) {
                    cur += Integer.parseInt(tmp[i]);
                } else {
                    cur -= Integer.parseInt(tmp[i]);
                }
            } else if (tmp[i].equals("?")) {
                pos++;
            } else {
                cur += Integer.parseInt(tmp[i]);
            }
        }
        int need = n - cur;

        int l = cur + pos;
        int r = cur + pos * n;
        int l1 = n + neg;
        int r1 = n + neg * n;
        boolean ok = r >= l1 && r1 >= l;
        int chose = choose(l, r, l1, r1);
        int need1 = 0, need2 = 0;
        for (int i = 1; i <= pos; i++) {
            int left = chose -  (pos - i) - cur;
            if(left >= i && left <= i*n){
                need1 = left;
                break;
            }
        }
        for (int i = 1; i <= neg; i++) {
            int left = chose -  (neg - i) - n;
            if(left >= i && left <= i*n){
                need2 = -left;
                break;
            }
        }
        if (ok) {
            out.println("Possible");
            for (int i = 0; i < tmp.length; i++) {
                if (tmp[i].equals("?")) {
                    if (need1 > 0 && (i == 0 || tmp[i - 1].equals("+"))) {
                        int v = Integer.min(need1, n);
                        need1 -= v;
                        out.print(v + " ");
                    } else if (need2 < 0 && i > 0 && tmp[i - 1].equals("-")) {
                        int v = Integer.min(-need2, n);
                        need2 += v;
                        out.print(v + " ");
                    } else {
                        out.print(1 + " ");
                    }
                } else {
                    out.print(tmp[i] + " ");
                }
            }
        } else {
            out.println("Impossible");
        }
        out.close();
    }

    static int choose(int l, int r, int l1, int r1) {
        if (l <= l1 && l1 <= r) {
            return l1;
        } else if (l <= r1 && r1 <= r) {
            return r1;
        } else if (l1 <= l && l <= r1) {
            return l;
        } else {
            return r;
        }
    }

    public static int[] KMP(String val) {
        int i = 0;
        int j = -1;
        int[] result = new int[val.length() + 1];
        result[0] = -1;
        while (i < val.length()) {
            while (j >= 0 && val.charAt(j) != val.charAt(i)) {
                j = result[j];
            }
            j++;
            i++;
            result[i] = j;
        }
        return result;

    }

    public static boolean nextPer(int[] data) {
        int i = data.length - 1;
        while (i > 0 && data[i] < data[i - 1]) {
            i--;
        }
        if (i == 0) {
            return false;
        }
        int j = data.length - 1;
        while (data[j] < data[i - 1]) {
            j--;
        }
        int temp = data[i - 1];
        data[i - 1] = data[j];
        data[j] = temp;
        Arrays.sort(data, i, data.length);
        return true;
    }

    public static int digit(long n) {
        int result = 0;
        while (n > 0) {
            n /= 10;
            result++;
        }
        return result;
    }

    public static double dist(long a, long b, long x, long y) {
        double val = (b - a) * (b - a) + (x - y) * (x - y);
        val = Math.sqrt(val);
        double other = x * x + a * a;
        other = Math.sqrt(other);
        return val + other;

    }

    public static class Point implements Comparable<Point> {

        int x, y;

        public Point(int start, int end) {
            this.x = start;
            this.y = end;
        }

        @Override
        public int hashCode() {
            int hash = 5;
            hash = 47 * hash + this.x;
            hash = 47 * hash + this.y;
            return hash;
        }

        @Override
        public boolean equals(Object obj) {
            if (obj == null) {
                return false;
            }
            if (getClass() != obj.getClass()) {
                return false;
            }
            final Point other = (Point) obj;
            if (this.x != other.x) {
                return false;
            }
            if (this.y != other.y) {
                return false;
            }
            return true;
        }

        @Override
        public int compareTo(Point o) {
            return Integer.compare(x, o.x);
        }
    }

    public static class FT {

        long[] data;

        FT(int n) {
            data = new long[n];
        }

        public void update(int index, long value) {
            while (index < data.length) {
                data[index] += value;
                index += (index & (-index));
            }
        }

        public long get(int index) {
            long result = 0;
            while (index > 0) {
                result += data[index];
                index -= (index & (-index));
            }
            return result;

        }
    }

    public static long gcd(long a, long b) {
        if (b == 0) {
            return a;
        }
        return gcd(b, a % b);
    }

    public static long pow(long a, long b, long MOD) {
        if (b == 0) {
            return 1;
        }
        if (b == 1) {
            return a;
        }
        long val = pow(a, b / 2, MOD);
        if (b % 2 == 0) {
            return val * val % MOD;
        } else {
            return val * (val * a % MOD) % MOD;

        }
    }

    static class Scanner {

        BufferedReader br;
        StringTokenizer st;

        public Scanner() throws FileNotFoundException {
            // System.setOut(new PrintStream(new BufferedOutputStream(System.out), true));
            br = new BufferedReader(new InputStreamReader(System.in));
            //  br = new BufferedReader(new InputStreamReader(new FileInputStream(new File("input.txt"))));
        }

        public String next() {

            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (Exception e) {
                    throw new RuntimeException();
                }
            }
            return st.nextToken();
        }

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

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

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

        public String nextLine() {
            st = null;
            try {
                return br.readLine();
            } catch (Exception e) {
                throw new RuntimeException();
            }
        }

        public boolean endLine() {
            try {
                String next = br.readLine();
                while (next != null && next.trim().isEmpty()) {
                    next = br.readLine();
                }
                if (next == null) {
                    return true;
                }
                st = new StringTokenizer(next);
                return st.hasMoreTokens();
            } catch (Exception e) {
                throw new RuntimeException();
            }
        }
    }
}
