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October 9 - BMTK Programming School, High League

Simple division

Integer division between a dividend n and a divisor d yields a quotient q and a remainder r. q is the integer which maximizes q · d such that q · dn and r = n - q · d.

For any set of integers there is an integer d such that each of the given integers when divided by d leaves the same remainder.


Each line contains a sequence of nonzero 32-bit signed integers separated by space. The last number on each line is 0 and this number does not belong to the sequence. There will be at least 2 and no more than 1000 numbers in a sequence; not all numbers occurring in a sequence are equal. The last line contains a single 0 and should not be processed.


For each input line, print the largest integer which when divided into each of the input integers leaves the same remainder.

Time limit 1 second
Memory limit 128 MiB
Input example #1
701 1059 1417 2312 0
14 23 17 32 122 0
14 -22 17 -31 -124 0
Output example #1