A triline is a line with the property that three times its slope is equal to the sum of its x- intercept and its y- intercept. For how many integers q with 1\le q\le10\:000 is there at least one positive integer p so that there is exactly one triline through (p,q)?
Answer Choices
A. 60
B. 57
C. 58
D. 61
E. 59