Codeforces Round #332 (Div. 2) B. Spongebob and Joke simulation

B. Spongebob and Joke

While Patrick is gone shopping, Spongebob decided to play a little trick on his friend. The naughty Sponge browsed through Patrick ' s personal stuff and found a sequencea1,a2,...,a m  of length  m , consisting of integers From 1 to  n , not necessarily distinct. Then he picked some Sequence  F 1, F 2, ..., f n  of length  n  and for each number  a i  got number  b I = F a i . To finish the prank he erased the initial sequence  a i .

It's hard-to-express how sad Patrick is when he returned home from shopping! We'll just say that Spongebob immediately got really sorry on what he had done and he's now trying to restore the OR Iginal sequence. Help him does this or determine, that's impossible.

Input

The first line of the input contains the integers n and m (1≤ n, m ≤100 -the lengths of sequences Fi and bi respectively.

The second line contains n integers, determining sequence F1, F2, ..., f n (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  A i , such that  b i = f a i  for all  i  from 1 to   m . Then Print  m  integers  a 1, a 2, ..., a m .

If There is multiple suitable sequences ai, print "ambiguity".

If Spongebob have made a mistake in his calculations and no suitable sequence ai exists, print " C9>impossible ".

Sample Test (s) input

3 3
3 2 1
1 2 3

Output

Possible

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 are replaced by 1 and vice versa, while 2 never changes. The answer exists and is unique.

In the second sample all numbers be replaced by 1, so it's impossible to unambiguously restore the original sequence .

In the third sample fI ≠3 for all i, so no sequence ai transforms to such bi and we can say for sure that Spongebob have made a mistake.

Test instructions

Give you b array, f array, construct an array of a to satisfy: bi = fai. There are multiple sets of conditions output ambiguity, a set of conditions output it, no output impossblie

Exercises

We mark the F-array, count to find the only one.

//1085422276#include <bits/stdc++.h>using namespaceStd;typedefLong Longll;#defineMem (a) memset (A,0,sizeof (a))#definePB Push_backinline ll read () {ll x=0, f=1;CharCh=GetChar ();  while(ch<'0'|| Ch>'9'){        if(ch=='-') f=-1; ch=GetChar (); }     while(ch>='0'&&ch<='9') {x=x*Ten+ch-'0'; ch=GetChar (); }returnx*F;}//****************************************Const intn=100000+ -;#defineMAXN 100000+5intH[n],ans[n],c[n],b[n],f[n];intMain () {intN=read (), m=read ();  for(intI=1; i<=n;i++) {scanf ("%d",&F[i]); H[f[i]]++; C[f[i]]=i; }     for(intI=1; i<=m;i++) {scanf ("%d",&B[i]); }intf=0, siz=0, cool=0;  for(intI=1; i<=m;i++) {        if(h[b[i]]>1) f=1; if(h[b[i]]==1&AMP;&AMP;!F) {ans[++siz]=C[b[i]];} if(h[b[i]]==0) cool=1; }    if(cool) {cout<<"Impossible"<<Endl; }    Else if(f) {cout<<"Ambiguity"<<Endl; }    Else{cout<<"Possible"<<Endl;  for(intI=1; i<=siz;i+=1) {cout<<ans[i]<<" "; }    }    return 0;}

Code

Codeforces Round #332 (Div. 2) B. Spongebob and Joke simulation