Suppose $k\_1,k\_2,k\_3,\ldots,k\_n$ are non-negative integer numbers such that sum $k\_1+k\_2+\cdots+k\_n$ is an odd number. Let $a\_1,a\_2,\ldots,a\_n$ be arbitrary numbers satisfied:
$$\frac {|a\_1-a\_2|}{k\_1}=\frac {|a\_2-a\_3|}{k\_2}=\cdots=\frac {|a\_{n-1}-a\_n|}{k\_{n-1}}=\frac {|a\_n-a\_1|}{k\_n}$$
How Prove that: $a\_1=a\_2=\cdots=a\_n$?