Multiple Blog pages and sidebars

I am trying to set up 2 separate blog pages.  The problem I am having is with the sidebar which shows the latest posts.  If I change which blog page it points to on one page, it changes on the other.  So that I can have blog page A with an index of items on page A, but then page B show a list of items on page A, not page B.  If I change the page source for the sidebar on page B, to page B, then it changes the sidebar on page A as well, so that it now shows post from page B only.  I could add two separate blocks to both pages - one for blog posts from page A and one for page B - but that is not really what I am after.  Any suggestions?

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