How to solve this problem using matrix exponentiation. The recurrence relation is :

f(n, k, 0) = 2 * f(n - 1, k, 1) + f(n - 1, k, 0)

f(n, k, 1) = f(n - 1, k, 1) + f(n - 1, k, 0)

1 < n < 1e9

1 < k < 1e3