Implement a Dynamic Todo List with React Hooks

You are tasked with building a simple TodoList component using React hooks. The component should allow users to add new items to a list and remove existing items. Your solution should: * Manage the list of items using the useState hook. * Properly handle input field state for new items. * Implement an addItem function that adds a new todo item to the list. * Implement a removeItem function that removes a todo item by its index. * Ensure state updates are immutable to prevent common React pitfalls and ensure optimal re-rendering behavior. The starter code provides a basic structure, but it contains several issues related to state management and immutability that need to be addressed.