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Professor Byteman Laugh has been given a unique chance. He has been told that he could get a million dollars for his research from Foundation for Helping Wicked Byteprofessors. The professor always does his best to make his research interesting. Now it is time for the society to grade the professor's work.
However, it is not so easy. The professor has only one week before he will have to present the results of his research. As every scientist, professor Laugh is a little bit absent-minded. He has lost the results somewhere, so he is asking you to write a program which reproduces them.
Professor Laugh does not like to bore his friends and colleagues. Therefore, he is not interested in ordinary integrals, but in thrilling and mind-blowing prime numbers.
For a prime number1 greater than , an integer greater than 1 and an integer less than the professor says that is -interesting if there is a natural number such that, In other words and give the same remainder when divided by .
Write a program which:
The first line contains two integers separated by a single space: a prime number and a number (). The second line contains one integer , i.e. the number of cases (). Each of next lines contains one integer. The -th of these lines contains a number , .
Your program should write exactly lines. The line number () should contain one word: TAK (i.e. yes in Polish) if is -interesting, NIE (i.e. no in Polish) if it is not.
For the input data:
17 2 5 1 9 3 7 6
the correct result is:
TAK TAK NIE NIE NIE
Task authors: Jakub Pawlewicz, Jakub Radoszewski (formulation by Szymon Wasik).