Find the Minimal Divisor with Equal Remainders

Given three positive integers \(a\), \(b\), and \(c\), and an integer \(x\) such that \(x > 1\), when \(a\), \(b\), and \(c\) are divided by \(x\), they all yield the same remainder. It is guaranteed that there exists a valid \(x\) satisfying this condition. Your task is to determine the smallest such \(x\) (i.e. the minimal \(x > 1\) ) that satisfies \(a \bmod x = b \bmod x = c \bmod x\).

Hint:

This condition is equivalent to requiring that \(x\) divides the differences \(|a - b|\), \(|b - c|\) and \(|a - c|\). Therefore, if \(d = \operatorname{gcd}(|a-b|, |b-c|, |a-c|)\), then the required \(x\) is the minimal divisor of \(d\) that is greater than \(1\). In the special case where \(a = b = c\), any \(x > 1\) works so the answer is \(2\).

inputFormat

The input consists of a single line containing three positive integers \(a\), \(b\), and \(c\) separated by spaces.

outputFormat

Output a single integer which is the smallest \(x > 1\) that satisfies the condition.

sample

5 15 10

5