Odd Revenue Marker Total

Context

A reporting system assigns meaning to positive odd-numbered revenue markers. Given the first and last marker numbers in a requested interval, calculate the total of every positive odd marker included by that interval. The report must answer instantly even when the bounds span a very large range.

Problem

Implement a function that returns the sum of all positive odd integers from lower_bound through upper_bound, including both endpoints when they qualify. Zero and negative integers never contribute. If lower_bound is greater than upper_bound, the interval is empty and the result is 0. Use an endpoint prefix calculation: determine the sum of qualifying odd positive integers through an endpoint, then subtract the prefix through the integer immediately before the lower bound from the prefix through the upper bound.

Examples

Constraints

• -1000000000 <= lower_bound <= 1000000000
• -1000000000 <= upper_bound <= 1000000000
• Types: lower_bound is int, upper_bound is int; result is int

Function signature

def sum_odd_markers(lower_bound: int, upper_bound: int) -> int

lower_bound int

The inclusive first integer in the report interval.

upper_bound int

The inclusive last integer in the report interval.

returns int

The exact sum of all positive odd integers in the inclusive interval, or 0 when the interval is empty or contains no positive odd integer.

Notes

• The result and intermediate values may be larger than either input bound.
• Python integer arithmetic provides the required exactness.