Let S be the set of lattice points in the coordinate plane, both of whose coordinates are integers between 1 and 30 , inclusive. Exactly 300 points in S lie on or below a line with equation y=m x. The possible values of m lie in an interval of length \dfrac{a}{b}, where a and b are relatively prime positive integers. What is a+b ?
Answer Choices
A. 31
B. 47
C. 62
D. 72
E. 85