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

B. Spongebob and Joke

time limit per test
2 seconds

memory limit per test
256 megabytes

input
standard input

output
standard output

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".

Sample test(s)

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.

题意：有数列f
, b[m], a[m]，f[ a[i] ] = b[i](1<= i <=m),已知n,m, f
, b[m]。求a[m],有多重可能输出Ambiguity， 不能求出输出Impossible,只有一种可能输出Possible和数列a[m]

三个输出就有三种情况。
情况一：Impossibleb[m]数列有的数，f
没有
情况二：Ambiguityb[m]数列有的数，f
全都有且其中有一个至少有两个

情况三：Possible
b[m]数列有的数，f
都有且f
中只有一个

当时做时以为，b[m]中的数x出现的次数大于f
中出现的次数就是Impossible,没有仔细考虑。