You are given an array of integers . Your task is to process queries:
add an integer to all elements of the array.
After each query, output the greatest common divisor of all elements of the array.
The first line contains two integers , () — the size of the array and the number of queries, respectively.
The second line contains integers () — the elements of the array .
Each of the next lines contains one integer ().
Output numbers — the greatest common divisor of the elements of the array after each addition.
After the first query because was added to each element. The greatest common divisor in it is .
After the second query because was added to each element. The greatest common divisor in it is .
After the third query because was added to each element. The greatest common divisor in it is .
In this problem, there are conditional blocks. If your solution works correctly for certain constraints, it will receive a certain number of points. Note that the evaluation is still in the testing phase.
( points): ;
( points): ;
( points): the number of different elements among is no more than ;
( points): without additional constraints.