Fibonacci Polynomial

The Fibonacci sequence is defined by `F_1 = F_2 = 1` and the recurrence relation `F_n = F_{n-1} + F_{n-2}` for every integer `n >= 3`. Given natural numbers `m,n >= 1`, find the minimum degree `d` such that there exists a polynomial `f(x) = a_d x^d + a_{d-1} x^{d-1} + ... + a_1 x + a_0` satisfying `f(k) = F_{m+k}` for all `k = 0,1,...,n`. Justify your answer.