如何仅用递归函数和栈操作逆序一个栈(不用额外空间)

int getStackBottomDate(Stack<Integer> stack) {
        int result = stack.pop();
        if (stack.isEmpty()) {
            return result;
        } else {
            int last = getStackBottomDate(stack);
            stack.push(result);
            return last;
        }
    }
    
    void reverseStack(Stack<Integer> stack) {
        if (stack.isEmpty()) {
            return;
        }
        int res = getStackBottomDate(stack);
        reverseStack(stack);
        stack.push(res);
    }