Let $a_1,a_2,a_3,\ldots,a_n$ be in A.P. If $\frac{1}{a_1a_n}+\frac{1}{a_2a_{n-1}}+\ldots+\frac{1}{a_na_1}=\frac{K}{a_1+a_n}\left(\frac{1}{a_1}+\frac{1}{a_2}+\ldots+\frac{1}{a_n}\right)$, then $K$ is equal to