Algorithm Speedup
Memory limit: 64 MB
As a punishment for misbehaving, Byteasar is to calculate a certain mysterious and nasty
Boolean-valued function , which is defined for a pair of positive integer sequences
, as follows:
boolean
if then return
else if then return
else return .
Where:
-
denotes the set of members of the sequence
(order and repetitions of elements are insignificant),
-
denotes the longest prefix (initial part of any length) of the sequence ,
such that ,
- denotes the longest suffix (final part of any length) of the sequence ,
such that ,
- denotes the logical conjunction, - true, - false,
and - cardinality of set .
For example, for the sequence
we have:
For very large data a programme calculating values of the function
directly from definition is too
slow by any standards.
Therefore you are to make these calculations as fast as possible.
Write a programme that
reads several pairs of sequences from the standard input and
prints out the values on the standard output for every input pair.
Input
The first line of the standard input contains one integer ()
denoting the number of sequence pairs to analyse.
Next line hold descriptions of test cases.
The first line of each description contains two integers and
() separated by a single space and denoting
the lengths of the first and second sequence, respectively.
The second line holds integers ()
that form the sequence , separated by single spaces.
The third line holds integers (),
that form the sequence , separated by single spaces.
Output
The output should consist of exactly lines; the -th line (for )
should contain a single integer - 0 or 1 -
the value of for -th test case.
Example
For the input data:
2
4 5
3 1 2 1
1 3 1 2 1
7 7
1 1 2 1 2 1 3
1 1 2 1 3 1 3
the correct result is:
0
1
Task authors: Jakub Radoszewski and Wojciech Rytter.