Problem Statement
A sequence is defined as:
- $g_k = 1$, for $0 \le k \le 1999$
- $g_k = g_{k-2000} + g_{k - 1999}$, for $k \ge 2000$.
Find $g_k \bmod 20092010$ for $k = 10^{9\times 2^N}$.
Submit Answers
You need to submit in the format: "N:problem(N)", possibly with multiple values at once, separated by commas, with $N$ between $1$ and $100$.