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.*;
import java.util.Arrays;
import java.util.StringTokenizer;

public class Div1A {

    public static void main(String[] args) throws IOException {
        Div1A solver = new Div1A();
        solver.solve();
    }

    private void solve() throws IOException {
        BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
//        BufferedReader reader = new BufferedReader(new StringReader("? + ? - ? + ? + ? = 42"));
//        BufferedReader reader = new BufferedReader(new StringReader("? + ? - ? = 3"));
//        BufferedReader reader = new BufferedReader(new StringReader("? = 1000000"));
//        BufferedReader reader = new BufferedReader(new StringReader("? - ? = 1"));

        String line = reader.readLine();

        FastScanner sc = new FastScanner(line);

        int N = 1;
        int M = 0;
        int X = 0;
        while (true) {
            String token = sc.next();

            char c = token.charAt(0);

            if (c == '+') ++N;
            if (c == '-') ++M;
            if (c == '=') {
                X = sc.nextInt();
                break;
            }
        }

//        System.out.println(N);
//        System.out.println(M);
//        System.out.println(X);

        int lo = 1;
        int hi = 2000000000;
        int S = -1;
        while (lo + 1 < hi) {
            int mid = (lo + hi + 1) / 2;
            int ac = check(X, N, mid);
            int bc = check(X, M, mid - X);

            if (ac > 0) {
                if (bc >= 0) {
                    hi = mid;
                } else {
                    break;
                }
            } else if (ac < 0) {
                if (bc <= 0) {
                    lo = mid;
                } else {
                    break;
                }
            } else { // == 0
                if (bc > 0) {
                    hi = mid;
                } else if (bc < 0) {
                    lo = mid;
                } else {
                    S = mid;
                    break;
                }
            }
        }

        if (S >= 0) {
            // Possible
            System.out.println("Possible");

            int[] a = find(N, X, S);
            int[] b = find(M, X, S - X);

//            System.out.println(S);
//            System.out.println(Arrays.toString(a));
//            System.out.println(Arrays.toString(b));

            FastScanner sc2 = new FastScanner(line);
            int ap = 0;
            int bp = 0;
            System.out.print(a[ap++]);
            while (true) {
                String token = sc2.next();

                char c = token.charAt(0);

                if (c == '+') System.out.print(" + " + a[ap++]);
                if (c == '-') System.out.print(" - " + b[bp++]);
                if (c == '=') {
                    System.out.println(" = " + X);
                    break;
                }
            }

        } else {
            // Impossible
            System.out.println("Impossible");
        }

    }

    private int[] find(int N, int X, int S) {
        int[] a = new int[N];

        int rest = S;
        for (int i = 0; i < N; i++) {
            int d = Math.min(X, rest - (N - (i + 1)));
            a[i] = d;
            rest -= d;
        }

        return a;
    }

    private int check(int X, int N, int S) {
        if (N > S) return -1;
        if (X * N < S) return 1;
        return 0;
    }

    private static class FastScanner {
        private BufferedReader br;
        private StringTokenizer st;

        public FastScanner(InputStream in) throws IOException {
            br = new BufferedReader(new InputStreamReader(in));
        }

        public FastScanner(File file) throws IOException {
            br = new BufferedReader(new FileReader(file));
        }

        public FastScanner(String s) {
            br = new BufferedReader(new StringReader(s));
        }

        public String next() {
            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                    return "";
                }
            }
            return st.nextToken();
        }

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

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

}
