In \triangle Q R S, point T is on Q S with \angle Q R T=\angle S R T. Suppose that Q T=m and T S=n for some integers m and n with n>m and for which n+m is a multiple of n-m. Suppose also that the perimeter of \triangle Q R S is p and that the number of possible integer values for p is m^{2}+2 m-1. The value of n-m is
Answer Choices
A. 4
B. 1
C. 3
D. 2
E. 5