Compute product excluding index without division

Given an integer array nums, return an array ans where ans[i] equals the product of all elements of nums except nums[i], without using division. Achieve O(n) time and O( 1) extra space beyond the output array. Perform a step-by-step dry run showing how prefix and postfix accumulators update at each index. Explain how your solution handles zeros and negative numbers and how you would mitigate overflow in languages with fixed-width integers.