CMIMC 2021 Algebra and Number Theory Division 1 Problem 5

Suppose f is a degree 42 polynomial such that for all integers 0 \leq i \leq 42,

f(i)+f(43+i)+f(2 \cdot 43+i)+\cdots+f(46 \cdot 43+i)=(-2)^{i}

Find f(2021)-f(0).