How to get first heading in each column?

Hello. If there is no heading in a column, what should be displayed? What about numbering? There is a very similar question in How to get the number of the first and last paragraph on a page and show the result in the header?.

#set page(header: [Heading 1#h(1fr)Heading 2], columns: 2)
#set par(justify: true)

= Heading 1
#lorem(50)

#lorem(60)

#lorem(70)

#lorem(80)

#lorem(50)

= Heading 2
#lorem(60)

#lorem(70)

#lorem(80)

#lorem(70)

Is this how it should look like?