Triangle  ABC  has side lengths $AB=7,BC=8$  and $CA=9.$  Circle  ${\omega }_1$ passes through  B and is tangent to line AC  at A.  Circle  ${\omega }_2$ passes through C  and it tangent to line AB  at A.  Let K  be in the intersection of circles  ${\omega }_1$ and  ${\omega }_2$ ( K is different from  A). Then  $AK=\frac{m}{n},$ where  m and n  are relatively prime positive integers. The value of  $m-n$ is equal to _____