In the diagram, P Q is a diameter of the circular base of the cylinder. R S is a diameter of the top face of the cylinder and is directly above P Q, as shown. Point U is on the circumference of the top face, halfway between R and S. Point T is on the cylinder and is directly above P. Suppose that Q S=m and P T=n, where m and n are integers with 1<n<m. If Q U=9 \sqrt{33} and U T=40, what is the remainder when the integer equal to Q T^{2} is divided by 100?
Answer Choices
A. 29
B. 49
C. 9
D. 89
E. 69