Consider a decreasing sequence of n positive integers x_{1}>x_{2}>\cdots>x_{n} that satisfies:
- The average of the first 3 terms is 2025.
- For all 4\le k\le n, the average of the first k terms is 1 less than the average of the first k-1 terms.
What is the greatest possible value of n?
Answer Choices:
A. 1013
B. 1014
C. 1016
D. 2016
E. 2025