Calculate the absolute distance `d = |endPos - startPos|`. If `(k - d)` is negative or odd, return 0 immediately since it's impossible to reach `endPos` in `k` steps.

The problem reduces to finding the number of ways to arrange `(k + d)/2` right moves and `(k - d)/2` left moves in a sequence of `k` steps. This is equivalent to choosing `(k + d)/2` positions out of `k` for the right moves (or left moves).

The solution can be computed using combinatorics: the result is `C(k, (k + d)/2) % (10^9 + 7)`, where `C(n, k)` is the binomial coefficient. Use dynamic programming or memoization to compute the binomial coefficient efficiently under modulo constraints.