Problem Narrative

You’re working on a fintech platform that processes millions of card authorizations per day. A legacy risk-throttling rule uses a Fibonacci-based backoff schedule to decide how long to delay repeated verification attempts for suspicious sessions. Because this function is called frequently in latency-sensitive paths, you need an implementation that is correct and efficient.

Task

Implement a function fib(n) that returns the nth Fibonacci number.

We define the Fibonacci sequence as:

• F(0) = 0
• F(1) = 1
• F(n) = F(n-1) + F(n-2) for n >= 2

Input

• An integer n (0-indexed)

Output

• Return F(n) as an integer.

Examples

Example 1

• Input: n = 0
• Output: 0
• Explanation: By definition, the 0th Fibonacci number is 0.

Example 2

• Input: n = 7
• Output: 13
• Explanation (step-by-step):
  • F(2)=1, F(3)=2, F(4)=3, F(5)=5, F(6)=8, F(7)=13.

Constraints

• 0 <= n <= 10^5

Notes / Clarifications

1. Your solution should be efficient enough to handle the upper bound without timing out.
2. Return the exact integer value (Python integers can grow arbitrarily large).
3. Avoid naive recursion without memoization, as it is exponential time.