While Patrick was gone shopping, Spongebob decided to play a little trick on his friend. The naughty Sponge browsed through Patrick's personal stuff and found a sequence a1, a2, ..., am of length m, consisting of integers from 1 to n, not necessarily distinct. Then he picked some sequence f1, f2, ..., fn of length n and for each number ai got number bi = fai. To finish the prank he erased the initial sequence ai.

It's hard to express how sad Patrick was when he returned home from shopping! We will just say that Spongebob immediately got really sorry about what he has done and he is now trying to restore the original sequence. Help him do this or determine that this is impossible.

Input

The first line of the input contains two integers n and m (1 ≤ n, m ≤ 100 000) — the lengths of sequences fi and bi respectively.

The second line contains n integers, determining sequence f1, f2, ..., fn (1 ≤ fi ≤ n).

The last line contains m integers, determining sequence b1, b2, ..., bm (1 ≤ bi ≤ n).

Output

Print "Possible" if there is exactly one sequence ai, such that bi = fai for all i from 1 to m. Then print m integers a1, a2, ..., am.

If there are multiple suitable sequences ai, print "Ambiguity".

If Spongebob has made a mistake in his calculations and no suitable sequence ai exists, print "Impossible".

Examples

Input

3 3
3 2 1
1 2 3


Output

Possible
3 2 1 


Input

3 3
1 1 1
1 1 1


Output

Ambiguity


Input

3 3
1 2 1
3 3 3


Output

Impossible

Note

In the first sample 3 is replaced by 1 and vice versa, while 2 never changes. The answer exists and is unique.

In the second sample all numbers are replaced by 1, so it is impossible to unambiguously restore the original sequence.

In the third sample fi ≠ 3 for all i, so no sequence ai transforms into such bi and we can say for sure that Spongebob has made a mistake.
import java.io.*;
import java.util.Arrays;
import java.util.Locale;

/**
 * @author master_j
 * @version 0.4.1
 * @since Mar 22, 2015
 */
public class Solution {
    private void solve() throws IOException {
        int n = io.nI(), m = io.nI();
        int[] f = io.nIa(n);
        int[] b = io.nIa(m);
        boolean[] ambig = new boolean[1 + n];
        int[] f_1 = new int[ambig.length];
        Arrays.fill(f_1, -1);
        for (int i = 0; i < f.length; i++)
            if (f_1[f[i]] == -1)
                f_1[f[i]] = 1 + i;
            else
                ambig[f[i]] = true;
        int[] a = new int[m];

        for (int i = 0; i < a.length; i++)
            if (f_1[b[i]] == -1) {
                io.wln("Impossible");
                return;
            }
        for (int i = 0; i < a.length; i++)
            if (ambig[b[i]]) {
                io.wln("Ambiguity");
                return;
            }

        for (int i = 0; i < a.length; i++)
            a[i] = f_1[b[i]];
        io.wln("Possible");
        for (int i : a) {
            io.w(i);
            io.w(' ');
        }
    }//2.2250738585072012e-308

    public static void main(String[] args) throws IOException {
        IO.launchSolution(args);
    }

    Solution(IO io) throws IOException {
        this.io = io;
        solve();
    }

    private final IO io;
}

class IO {
    static final String _localArg = "master_j";
    private static final String _problemName = "";
    private static final IO.Mode _inMode = Mode.STD_;
    private static final IO.Mode _outMode = Mode.STD_;
    private static final boolean _autoFlush = false;

    enum Mode {STD_, _PUT_TXT, PROBNAME_}

    private final StreamTokenizer st;
    private final BufferedReader br;
    private final Reader reader;

    private final PrintWriter pw;
    private final Writer writer;

    static void launchSolution(String[] args) throws IOException {
        boolean local = (args.length == 1 && args[0].equals(IO._localArg));
        IO io = new IO(local);

        long nanoTime = 0;
        if (local) {
            nanoTime -= System.nanoTime();
            io.wln("<output>");
        }

        io.flush();
        new Solution(io);
        io.flush();

        if (local) {
            io.wln("</output>");
            nanoTime += System.nanoTime();
            final long D9 = 1000000000, D6 = 1000000, D3 = 1000;
            if (nanoTime >= D9)
                io.wf("%d.%d seconds\n", nanoTime / D9, nanoTime % D9);
            else if (nanoTime >= D6)
                io.wf("%d.%d millis\n", nanoTime / D6, nanoTime % D6);
            else if (nanoTime >= D3)
                io.wf("%d.%d micros\n", nanoTime / D3, nanoTime % D3);
            else
                io.wf("%d nanos\n", nanoTime);
        }

        io.close();
    }

    IO(boolean local) throws IOException {
        if (_inMode == Mode.PROBNAME_ || _outMode == Mode.PROBNAME_)
            if (_problemName.length() == 0)
                throw new IllegalStateException("You imbecile. Where's my <_problemName>?");

        if (_problemName.length() > 0)
            if (_inMode != Mode.PROBNAME_ && _outMode != Mode.PROBNAME_)
                throw new IllegalStateException("You imbecile. What's the <_problemName> for?");

        Locale.setDefault(Locale.US);

        if (local) {
            reader = new FileReader("input.txt");
            writer = new OutputStreamWriter(System.out);
        } else {
            switch (_inMode) {
                case STD_:
                    reader = new InputStreamReader(System.in);
                    break;
                case PROBNAME_:
                    reader = new FileReader(_problemName + ".in");
                    break;
                case _PUT_TXT:
                    reader = new FileReader("input.txt");
                    break;
                default:
                    throw new NullPointerException("You imbecile. Gimme _inMode.");
            }
            switch (_outMode) {
                case STD_:
                    writer = new OutputStreamWriter(System.out);
                    break;
                case PROBNAME_:
                    writer = new FileWriter(_problemName + ".out");
                    break;
                case _PUT_TXT:
                    writer = new FileWriter("output.txt");
                    break;
                default:
                    throw new NullPointerException("You imbecile. Gimme _outMode.");
            }
        }

        br = new BufferedReader(reader);
        st = new StreamTokenizer(br);

        pw = new PrintWriter(writer, _autoFlush);

        if (local && _autoFlush)
            wln("Note: auto-flush is on.");
    }

    //@formatter:off
    void wln()          {pw.println(); }
    void wln(boolean x) {pw.println(x);}
    void wln(char x)    {pw.println(x);}
    void wln(char x[])  {pw.println(x);}
    void wln(double x)  {pw.println(x);}
    void wln(float x)   {pw.println(x);}
    void wln(int x)     {pw.println(x);}
    void wln(long x)    {pw.println(x);}
    void wln(Object x)  {pw.println(x);}
    void wln(String x)  {pw.println(x);}

    void wf(String f, Object... o) {pw.printf(f, o);}

    void w(boolean x)   {pw.print(x);}
    void w(char x) {pw.print(x);}
    void w(char x[]) {pw.print(x);}
    void w(double x)    {pw.print(x);}
    void w(float x)     {pw.print(x);}
    void w(int x)       {pw.print(x);}
    void w(long x)      {pw.print(x);}
    void w(Object x)    {pw.print(x);}
    void w(String x)    {pw.print(x);}

    int nI() throws IOException {st.nextToken(); return (int)st.nval;}
    double nD() throws IOException {st.nextToken(); return st.nval;}
    float nF() throws IOException {st.nextToken(); return (float)st.nval;}
    long nL() throws IOException   {st.nextToken(); return (long)st.nval;}
    String nS() throws IOException {st.nextToken(); return st.sval;}

    int[] nIa(int n) throws IOException {
        int[] a = new int[n];
        for (int i = 0; i < n; i++)
            a[i] = nI();
        return a;
    }
    double[] nDa(int n) throws IOException {
        double[] a = new double[n];
        for (int i = 0; i < n; i++)
            a[i] = nD();
        return a;
    }
    String[] nSa(int n) throws IOException {
        String[] a = new String[n];
        for (int i = 0; i < n; i++)
            a[i] = nS();
        return a;
    }

    void wc(String x)         {wc(x.toCharArray());}
    void wc(char c1, char c2) {for (char c = c1; c<=c2; c++) wc(c);}
    void wc(char x[])         {for (char c : x) wc(c); }
    void wc(char x)           {st.ordinaryChar(x); st.wordChars(x, x);}

    public boolean eof() {return st.ttype == StreamTokenizer.TT_EOF;}
    public boolean eol() {return st.ttype == StreamTokenizer.TT_EOL;}

    void flush() {pw.flush();}
    void close() throws IOException {reader.close(); br.close(); flush(); pw.close();}
    //@formatter:on
}