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.util.*;
import java.math.*;
import java.io.*;
public class Luck{
	public static InputReader sc;
    public static PrintWriter out;
    public static final long MOD = (long) (1e9 + 7);
    static TreeSet<Integer>[] train;
    static TreeSet<Integer>[] bus;
    public static void main(String[] args){
    	sc=new InputReader(System.in);	
    	out=new PrintWriter(System.out);
    	int n=sc.nextInt();
    	int m=sc.nextInt();
    	int[] f=new int[n];
    	HashMap<Integer,Integer> map=new HashMap<Integer, Integer>();
    	HashMap<Integer,Integer> index=new HashMap<Integer, Integer>();
    	int flag=0;
    	for(int i=0;i<n;i++){
    		f[i]=sc.nextInt();
    		if(map.containsKey(f[i])){
    			map.put(f[i], map.get(f[i])+1);
    		}
    		else{
    			map.put(f[i], 1);
    			index.put(f[i], i+1);
    		}
    	}
    	int[] b=new int[m];
    	int[] ans=new int[m];
    	for(int i=0;i<m;i++){
    		b[i]=sc.nextInt();
    	}
    	for(int i=0;i<m;i++){
    		if(!map.containsKey(b[i])){
    			flag=2;
    			break;
    		}
    		else if(map.get(b[i])>1){
    			flag=1;
    		}
    		else{
    			ans[i]=index.get(b[i]);
    		}
    	}
    	if(flag==1){
    		out.println("Ambiguity");
    	}
    	else if(flag==2){
    		out.println("Impossible");
    	}
    	else{
    		out.println("Possible");
    		for(int i=0;i<m;i++){
    			out.print(ans[i]+" ");
    		}
    		out.println();
    	}
    	out.close();
    }
 
    static class Pair{
    	int profit;
    	int val;
    	Pair(){
    		this.profit=-1;
    		this.val=-1;
    	}
    	Pair(int profit,int val){
    		this.profit=profit;
    		this.val=val;
    	}
    	public static Comparator<Pair> Val=new Comparator<Pair>(){
    		public int compare(Pair p1,Pair p2){
    			return (int)p1.profit-(int)p2.profit;
    		}
    	};
    	public int hashCode() {
    		final int prime = 31;
    		int result = 1;
    		result = prime * result + profit;
    		result = prime * result + val;
    		return result;
    	}
    	public boolean equals(Object obj){
    		if (this == obj)
    	        return true;
    	    if (!(obj instanceof Pair)) {
    	        return false;
    	    }
    	 
    	    Pair p = (Pair) obj;
    	    if(p.profit!=this.profit){
    	    	return false;
    	    }
    	    else if(p.val!=p.val){
    	    	return false;
    	    }
    	    return true;
    	}
    }
//    static int val;
//    static class DisjointSet{
//    	int n;
//    	int[] par;
//    	int[] rank;
//    	DisjointSet(int n){
//    		this.n=n;
//    		this.par=new int[n];
//    		this.rank=new int[n];
//    		makeSet();
//    	}
//    	void makeSet(){
//    		for(int i=1;i<n;i++){
//    			par[i]=i;
//    			rank[i]=1;
//    		}
//    	}
//    	void union(int x,int y){
//    		int parX=parent(x);
//    		int parY=parent(y);
//    		if(parX!=parY){
//    			if(rank[parX]>=rank[parY]){
//    				rank[parX]+=rank[parY];
//    				rank[parY]=0;
//    				par[parY]=parX;
//    			}
//    			else{
//    				rank[parY]+=rank[parX];
//    				rank[parX]=0;
//    				par[parX]=parY;
//    			}
//    			val-=1;
//    		}
//    	}
//    	int parent(int c){
//    		int i=c;
//    		while(i!=par[i]){
//    			i=par[i];
//    		}
//    		return i;
//    	}
//    }
    static int gcd(int a,int b){
    	if(b==0){
    		return a;
    	}
    	return gcd(b,a%b);
    	
    }
    static int lcm(int a,int b){
    	int g;
    	if(a<b){
    		g=gcd(b,a);
    	}
    	else{
    		g=gcd(a,b);
    	}
    	return (a*b)/g;
    }
    static long bigmod ( long a, long p, long m ) {
        long res = 1 % m, x = a % m;
        while ( p>0 ) {
            if ( (p & 1)==1 ) res = ( res * x ) % m;
            x = ( x * x ) % m; p >>= 1;
        }
        return res;
    }
    static boolean isPrime(int n){
    	 if (n == 2)
    	        return true;
    	    for (long i = 2; i * i <= n; i++) {
    	        if (n % i == 0)
    	            return false;
    	    }
    	    return true;
    }
    
    static void shuffle(int[] A){
    	for(int i=A.length-1;i>0;i--){
    		int j=(int)(Math.random()*(i+1));
    		int temp=A[j];
    		A[j]=A[i];
    		A[i]=temp;
    	}
    }
    
	public static class Node implements Comparable<Node>{
	    int u;
	    int v;
	    public Node(){
	    	;
	    }
	    public Node (int u, int v) {
	    	this.u = u;
	        this.v = v;
	    }
	    
	    public void print() {
	        out.println(v + " " + u + " ");
	    }
	   
	    public int compareTo(Node n1){
	    	return this.u-n1.u;
	    }
	}
	public static long pow(long base,long exp,long mod){
		if(exp==0){
			return 1;
		}
		if(exp==1){
			return base;
		}
		long temp=exp/2;
		long val=pow(base,temp,mod);
		long result=val*val;
		result=(result%mod);
		long AND=exp&1;
		if(AND==1){
			result*=base;
			result=(result%mod);
		}
		return result;
	}
	public static BigInteger pow(BigInteger base, BigInteger exp) {
	    if(exp.equals(new BigInteger(String.valueOf(0)))){
	        return new BigInteger(String.valueOf(1));
	    }    
	    if(exp.equals(new BigInteger(String.valueOf(1))))
	        return base;
	    BigInteger temp=exp.divide(new BigInteger(String.valueOf(2)));
	    BigInteger val = pow(base, temp);
	    BigInteger result = val.multiply(val);
	    result=result.remainder(new BigInteger(String.valueOf(MOD)));
	    BigInteger AND=exp.and(new BigInteger(String.valueOf(1)));
	    if(AND.equals(new BigInteger(String.valueOf(1)))){
	        result = result.multiply(base);
	        result=result.remainder(new BigInteger(String.valueOf(MOD)));
	    }    
	    return result;
	}
	    
	static class InputReader {

	    private InputStream stream;
	    private byte[] buf = new byte[8192];
	    private int curChar, snumChars;
	    private SpaceCharFilter filter;

	    public InputReader(InputStream stream) {
	        this.stream = stream;
	    }

	    public int snext() {
	        if (snumChars == -1)
	            throw new InputMismatchException();
	        if (curChar >= snumChars) {
	            curChar = 0;
	            try {
	                snumChars = stream.read(buf);
	            } catch (IOException e) {
	                throw new InputMismatchException();
	            }
	            if (snumChars <= 0)
	                return -1;
	        }
	        return buf[curChar++];
	    }

	    public int nextInt() {
	        int c = snext();
	        while (isSpaceChar(c))
	            c = snext();
	        int sgn = 1;
	        if (c == '-') {
	            sgn = -1;
	            c = snext();
	        }
	        int res = 0;
	        do {
	            if (c < '0' || c > '9')
	                throw new InputMismatchException();
	            res *= 10;
	            res += c - '0';
	            c = snext();
	        } while (!isSpaceChar(c));
	        return res * sgn;
	    }

	    public long nextLong() {
	        int c = snext();
	        while (isSpaceChar(c))
	            c = snext();
	        int sgn = 1;
	        if (c == '-') {
	            sgn = -1;
	            c = snext();
	        }
	        long res = 0;
	        do {
	            if (c < '0' || c > '9')
	                throw new InputMismatchException();
	            res *= 10;
	            res += c - '0';
	            c = snext();
	        } while (!isSpaceChar(c));
	        return res * sgn;
	    }

	    public int[] nextIntArray(int n) {
	        int a[] = new int[n];
	        for (int i = 0; i < n; i++)
	            a[i] = nextInt();
	        return a;
	    }

	    public String readString() {
	        int c = snext();
	        while (isSpaceChar(c))
	            c = snext();
	        StringBuilder res = new StringBuilder();
	        do {
	            res.appendCodePoint(c);
	            c = snext();
	        } while (!isSpaceChar(c));
	        return res.toString();
	    }

	    public boolean isSpaceChar(int c) {
	        if (filter != null)
	            return filter.isSpaceChar(c);
	        return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
	    }

	    public interface SpaceCharFilter {
	        public boolean isSpaceChar(int ch);
	    }
	}

}

