## A lagged Fibonacci sequence

### Problem 258

A sequence is defined as:

`g`_{k}= 1, for 0 ≤`k`≤ 1999`g`_{k}=`g`_{k-2000}+`g`_{k-1999}, for`k`≥ 2000.

Find `g`_{k} mod 20092010 for `k` = 10^{18}.

A sequence is defined as:

`g`_{k}= 1, for 0 ≤`k`≤ 1999`g`_{k}=`g`_{k-2000}+`g`_{k-1999}, for`k`≥ 2000.

Find `g`_{k} mod 20092010 for `k` = 10^{18}.