## Degree Four Recurrence

The sequence \(1, 1, 1, 1, 4, 7, \ldots\) is defined by: \(f(1) = f(2) = f(3) = f(4) = 1\), and \(f(n+4) = f(n) + f(n+1) + f(n+2) + f(n+3)\) for all positive integers \(n\).

Part A | Determine \(f(100)\). | |
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Part B | What is the remainder when \(f(2022^{2022})\) is divided by \(10^9+7\)? |