A lattice point in an x y-coordinate system is any point (x, y) where both x and y are integers. The graph of y=m x+2 passes through no lattice point with 0<x \leq 100 for all m such that \dfrac{1}{2}<m<a. What is the maximum possible value of a ?

**Answer Choices**

A. \dfrac{51}{101}

B. \dfrac{50}{99}

C. \dfrac{51}{100}

D. \dfrac{52}{101}

E. \dfrac{13}{25}