CF763C Timofey and remoduling

Little Timofey likes integers a lot. Unfortunately, he is very young and can't work with very big integers, so he does all the operations modulo his favorite prime $ m $ . Also, Timofey likes to look for arithmetical progressions everywhere. One of his birthday presents was a sequence of distinct integers $ a_{1},a_{2},...,a_{n} $ . Timofey wants to know whether he can rearrange the elements of the sequence so that is will be an arithmetical progression modulo $ m $ , or not. Arithmetical progression modulo $ m $ of length $ n $ with first element $ x $ and difference $ d $ is sequence of integers $ x,x+d,x+2d,...,x+(n-1)·d $ , each taken modulo $ m $ .

The first line contains two integers $ m $ and $ n $ ( $ 2

Print -1 if it is not possible to rearrange the elements of the sequence so that is will be an arithmetical progression modulo $ m $ . Otherwise, print two integers — the first element of the obtained progression $ x $ ( $ 0