Problem

In a Meta-style feed processing task, you are given a list of integers and need to shift all non-zero values to the left side of the list while keeping their original relative order. All zeros should be moved to the right.

Write a function that modifies the list in place and returns it.

Formal Specification

• Input: A list of integers nums
• Output: The same list after all non-zero elements have been moved to the left and all zeros moved to the right
• The relative order of non-zero elements must remain unchanged

Examples

Example 1

• Input: nums = [0, 1, 0, 3, 12]
• Output: [1, 3, 12, 0, 0]
• Explanation: The non-zero values 1, 3, and 12 stay in the same order and are compacted to the left.

Example 2

• Input: nums = [4, 0, 5, 0, 0, 2]
• Output: [4, 5, 2, 0, 0, 0]
• Explanation: All non-zero values are moved forward, and the remaining positions are filled with zeros.

Constraints

• 1 <= len(nums) <= 10^5
• -10^9 <= nums[i] <= 10^9
• The solution should run in linear time
• Use constant extra space beyond the input list