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.*;
import java.math.*;
import java.text.DecimalFormat;
import java.text.NumberFormat;
 

@SuppressWarnings("unchecked")
public class Main {
      
    int mod = 1000000007;

    public class SegmentTree{

       int n;
       int[] tree;

       SegmentTree(int[] arr){

          this.n = arr.length; 
          this.tree = new int[2 * n];

          for(int i = n; i < 2 * n; i++){
              this.tree[i] = arr[i - n];
          }

          for(int i = n - 1; i >= 1; i--){
              this.tree[i] = Math.min(this.tree[2 * i], this.tree[2 * i + 1]);
          }

       }

       public boolean isIn(int a){

          a += n;
          return tree[a] >= 1000000;

       }

       public int query(int l, int r){

          int res = Integer.MAX_VALUE;
          l = l + n;
          r = r + n;

          while(l < r){

              if(l % 2 == 1){
                  res = Math.min(res, tree[l]); 
                  l++;
              }

              if(r % 2 == 1){
                  r--;
                  res = Math.min(res, tree[r]);
              }

              l /= 2;
              r /= 2;
          }

          return res;
       }

       public void update(int idx, int v){
          
          idx += n; this.tree[idx] += v;
          while(idx > 1){
             idx /= 2;
             this.tree[idx] = Math.min(this.tree[2 * idx], this.tree[2 * idx + 1]);
          }
       }


    }

    public void solve() throws IOException{
    
       int n = in.nextInt();
       int m = in.nextInt();
       List<Integer> res = new ArrayList<>();
      
       HashMap<Integer, List<Integer>> fmap = new HashMap<>();
       for(int i = 0; i < n; i++){
          int f = in.nextInt();
          if(!fmap.containsKey(f)){
             fmap.put(f, new ArrayList<>());
          }
          fmap.get(f).add(i + 1);
       }
       
       boolean isAmb = false;

       Set<Integer> bset = new HashSet<>();
       for(int i = 0; i < m; i++){
          int b = in.nextInt();
          if(!fmap.containsKey(b)){
              out.println("Impossible");
              return;
          }else if(fmap.get(b).size() > 1){
             isAmb = true; 
          }else{
              res.add(fmap.get(b).get(0));
          }
          
       }

       if(isAmb){
         out.println("Ambiguity");
         return;
       }

       out.println("Possible");
       for(int i = 0; i < m; i++){
         out.print(res.get(i) + " ");
       }
       
    }




    FastScanner in;
    PrintWriter out;
    
    static class FastScanner {
 
        BufferedReader br;
        StringTokenizer st;
 
        FastScanner(InputStream in) {
            br = new BufferedReader(new InputStreamReader(in));
            st = null;
        }
 
        String next() throws IOException {
            while (st == null || !st.hasMoreTokens())
                st = new StringTokenizer(br.readLine());
            return st.nextToken();
        }
 
        String nextLine() throws IOException {
            if (st == null || !st.hasMoreTokens())
                return br.readLine();
            StringBuilder result = new StringBuilder(st.nextToken());
            while (st.hasMoreTokens()) {
                result.append(" ");
                result.append(st.nextToken());
            }
            return result.toString();
        }
 
        int nextInt() throws IOException {
            return Integer.parseInt(next());
        }
 
        long nextLong() throws IOException {
            return Long.parseLong(next());
        }
 
        double nextDouble() throws IOException {
            return Double.parseDouble(next());
        }
 
    }
 
    void run() throws IOException {
        in = new FastScanner(System.in);
        out = new PrintWriter(System.out, false);
        solve();
        out.close();
    }
 
    public static void main(String[] args) throws IOException{
        new Main().run();
    }
 
    public void printArr(int[] arr){
        for(int i = 0; i < arr.length; i++){
            out.print(arr[i] + " ");
        }
        out.println();
    }
 
    public long gcd(long a, long b){
        if(a == 0) return b;
        return gcd(b % a, a);
    }

    public boolean isPrime(long num){

        if(num == 0 || num == 1){
            return false;
        }

        for(int i = 2; i * i <= num; i++){
            if(num % i == 0){
                return false;
            }
        }

        return true;
    }

    public class Pair<A, B>{
        public A x; 
        public B y;

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

        @Override
        public boolean equals(Object o) {
            if (this == o) return true;
            if (o == null || getClass() != o.getClass()) return false;
            Pair<?, ?> pair = (Pair<?, ?>) o;
            if (!x.equals(pair.x)) return false;
            return y.equals(pair.y);
        }

        @Override
        public int hashCode() {
            int result = x.hashCode();
            result = 31 * result + y.hashCode();
            return result;
        }

    }

    class Tuple{
        int x; int y; int z;
        Tuple(int ix, int iy, int iz){
            x = ix;
            y = iy;
            z = iz;
        }
    }
}
