Functions f and g are quadratic, g(x)=-f(100-x), and the graph of g contains the vertex of the graph of f. The four x-intercepts on the two graphs have x-coordinates x_{1}, x_{2}, x_{3}, and x_{4}, in increasing order, and x_{3}-x_{2}=150. The value of x_{4}-x_{1} is m+n \sqrt{p}, where m, n, and p are positive integers, and p is not divisible by the square of any prime. What is m+n+p ?
Answer Choices
A. 602
B. 652
C. 702
D. 752
E. 802