# 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** · **d** ≤ **n** 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.

#### Input

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.

#### Output

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

701 1059 1417 2312 0 14 23 17 32 122 0 14 -22 17 -31 -124 0 0

179 3 3